[User]
For the function f(x) = -2|(3(-3sin(2πx + 3) - 1) - 5) + 2| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = (-1(1cos(2π(1|(-5x^2 - 1x) + 1| - 2)) + 1) - 2)/(1(1cos(2π(1|(-5x^2 - 1x) + 1| - 2)) + 1) + 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3|(2sin(3π(-1x - 4) - 3) + 3) - 2| - 1 is strictly decreasing.

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[User]
For the function f(x) = -2sin(1π(4((-2x)/(-1x - 3))^2 + 3((-2x)/(-1x - 3)) - 3) + 1) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 1cos(2π(-2|(1x + 1) + 1| + 3) - 2) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(2cos(1π((2x)/(-1x - 2)) - 1)) + 2| - 1 is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3(1sin(3π(-1|x + 3| - 2)) - 3)^2 + 4(1sin(3π(-1|x + 3| - 2)) - 3) - 2 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -2|((-3(1sin(3π(2x - 2) - 2) + 1) + 3)/(-2(1sin(3π(2x - 2) - 2) + 1) - 2)) + 1| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2((2(-1sin(1πx + 3) + 2))/(-2(-1sin(1πx + 3) + 2) + 3))^2 + 4((2(-1sin(1πx + 3) + 2))/(-2(-1sin(1πx + 3) + 2) + 3)) - 2 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 3cos(3π(-3((-3(2|x + 2| + 2) - 1)/(-1(2|x + 2| + 2) - 1)) - 3) - 1) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|(-3cos(3π(-5(-4x^2 + 3x - 3) - 2) - 3) - 2) - 1| + 2 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3(-2sin(1π(3x - 5) - 1) + 1) + 3)/(-2(-2sin(1π(3x - 5) - 1) + 1) + 1) positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 5(1sin(3π(-3|((-3x + 2)/(2x + 3)) + 2| + 3) + 3))^2 - 3(1sin(3π(-3|((-3x + 2)/(2x + 3)) + 2| + 3) + 3)) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3((-2(-1cos(1π(2|x - 2| - 1) - 3) - 1) - 3)/(1(-1cos(1π(2|x - 2| - 1) - 3) - 1) + 2)) + 5 negative?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3((-1(-2sin(1π(2x - 5) + 1) - 1) - 2)/(3(-2sin(1π(2x - 5) + 1) - 1) + 1))^2 + 2((-1(-2sin(1π(2x - 5) + 1) - 1) - 2)/(3(-2sin(1π(2x - 5) + 1) - 1) + 1)) + 3 is strictly decreasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2cos(3π(4(2|x| - 2) - 1) + 2) + 3 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(-4(1sin(2πx - 3) + 2) + 2)^2 - 4(-4(1sin(2πx - 3) + 2) + 2) + 5 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -1(1cos(2π(1((-2x + 1)/(2x + 1)) + 5) - 1) - 1)^2 + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2cos(2π(5(1|x - 1| + 1)^2 - 3(1|x - 1| + 1) - 1) - 2) + 3 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = (1(-2cos(1π(5x + 2) - 2) + 3) - 2)/(3(-2cos(1π(5x + 2) - 2) + 3) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2sin(3π(-4((-1x + 1)/(3x - 2)) + 2) - 2) - 2 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1sin(1π(-2|(-1x + 5) - 1| - 2)) + 1 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1cos(3π(1|(5(4x^2 - 2x + 5) + 5) + 1| - 2) + 2) + 2 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|(-2cos(1π(-4x^2 - 5x) - 1) + 3) - 1| + 1 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -5(-3cos(2π(1|x - 1| - 2) + 1)) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(-2(-2cos(1πx - 3) + 3) + 2) - 2)/(-3(-2(-2cos(1πx - 3) + 3) + 2)) is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2(3|(-1sin(2πx + 3) - 1) - 2|) - 5 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3sin(1π(1(1((3x - 3)/(-1x + 3)) + 1)^2 - 5(1((3x - 3)/(-1x + 3)) + 1) + 5) - 1) + 2 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(1|(-5(-2cos(1πx + 3))^2 + 4(-2cos(1πx + 3)) + 3) + 3|))/(3(1|(-5(-2cos(1πx + 3))^2 + 4(-2cos(1πx + 3)) + 3) + 3|) + 3) is strictly increasing.

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[User]
For the function f(x) = 2|((-2(3cos(1πx + 3) + 3) - 1)/(-1(3cos(1πx + 3) + 3) - 2)) + 2| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(-4(1cos(3π(-3x - 3) - 2))^2 - 5(1cos(3π(-3x - 3) - 2)) - 1) - 2| + 1 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 1|(-3sin(1π(2x - 5) + 3) + 2) - 3| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(-2cos(3π((1(2|x + 2|) - 3)/(2(2|x + 2|) - 1)) + 3) + 1)^2 + 5(-2cos(3π((1(2|x + 2|) - 3)/(2(2|x + 2|) - 1)) + 3) + 1) + 5 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 1sin(3π((-3(-4x^2 - 4x - 3) - 1)/(1(-4x^2 - 4x - 3) - 2)) - 3) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(-3(-2sin(2π(4x)) + 3)^2 + 5(-2sin(2π(4x)) + 3) - 1) + 2)/(-3(-3(-2sin(2π(4x)) + 3)^2 + 5(-2sin(2π(4x)) + 3) - 1) + 2) positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = (2(-3cos(3π(1|x + 1| + 2) + 2) + 3))/(-2(-3cos(3π(1|x + 1| + 2) + 2) + 3) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|((2(4(-2cos(3πx + 3) + 3) + 4) + 3)/(1(4(-2cos(3πx + 3) + 3) + 4))) + 2| + 1 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 2sin(3π(1((3x + 3)/(-3x + 1))^2 + 5((3x + 3)/(-3x + 1))) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(-1|(2sin(3πx + 1) - 3) + 3| - 2) + 2)/(-3(-1|(2sin(3πx + 1) - 3) + 3| - 2) + 2) positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 5(-1sin(2π(-1|x + 3| + 1) + 2) + 1) - 3 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 3(-5(-1cos(2πx - 2) - 3) + 1)^2 - 3(-5(-1cos(2πx - 2) - 3) + 1) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(3((3(3sin(1πx - 2) + 3) - 3)/(-3(3sin(1πx - 2) + 3))) - 4)^2 + 5(3((3(3sin(1πx - 2) + 3) - 3)/(-3(3sin(1πx - 2) + 3))) - 4) is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1sin(2π(3(-2|x + 1|)^2 - 1(-2|x + 1|) - 3) - 1) + 1 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -4((-1(-3sin(3π(-3|x + 2| + 2))) + 2)/(3(-3sin(3π(-3|x + 2| + 2))) + 1)) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3((1(-2cos(1πx + 3) + 1) + 1)/(-2(-2cos(1πx + 3) + 1) + 3)) + 3 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|(5(3sin(3πx - 2) - 2)^2 - 5(3sin(3πx - 2) - 2) - 3) + 1| - 2 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(2π(-4((3(-2|x| + 3) - 2)/(1(-2|x| + 3) + 2)) - 5) - 2) - 1 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3((3(3cos(3π(4x^2 + 5x - 3) + 2) - 3) - 1)/(2(3cos(3π(4x^2 + 5x - 3) + 2) - 3))) - 1 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1cos(2π(-5(1(2|x| - 3)^2 + 1(2|x| - 3) + 3) + 1) - 1) - 1 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-2|((-2(-2cos(3πx - 2) + 2) - 2)/(-3(-2cos(3πx - 2) + 2) - 2)) - 1| - 3) + 4 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(-1(1sin(1π(1|x - 3|) - 3) + 2) - 3)^2 + 4(-1(1sin(1π(1|x - 3|) - 3) + 2) - 3) + 2 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(-3cos(3π(1((3x - 3)/(-1x + 2))^2 - 3((3x - 3)/(-1x + 2)) - 2) + 3) + 1) + 4 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(-3|(-3(3cos(1πx - 1) + 2)^2 - 5)| - 2) - 1 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -2cos(3π((-2(2|(2x^2 - 5x) - 1|) + 1)/(1(2|(2x^2 - 5x) - 1|) - 3)) + 1), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(2|((-3(2cos(3πx - 3) - 3) + 2)/(-2(2cos(3πx - 3) - 3) - 2)) - 3| + 3)^2 + 3(2|((-3(2cos(3πx - 3) - 3) + 2)/(-2(2cos(3πx - 3) - 3) - 2)) - 3| + 3) + 3 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(-2|(2cos(1πx + 1) - 3)| + 3) + 2)/(-1(-2|(2cos(1πx + 1) - 3)| + 3) - 3) is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|((-1(1(2cos(1πx - 1) + 1)^2 + 3) + 1)/(-3(1(2cos(1πx - 1) + 1)^2 + 3) + 2)) + 1| + 2 is strictly decreasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3((-2(-2sin(1πx) + 3) + 2)/(-2(-2sin(1πx) + 3) - 1)) - 1 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1sin(3π(-2(-2|x - 2| - 2) + 3)) - 3 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(5(-1sin(2π(-3|x + 1| + 1) - 2) - 3)^2 - 3(-1sin(2π(-3|x + 1| + 1) - 2) - 3) - 2))/(2(5(-1sin(2π(-3|x + 1| + 1) - 2) - 3)^2 - 3(-1sin(2π(-3|x + 1| + 1) - 2) - 3) - 2) + 2) positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 2cos(1π(4((2(3|x + 2| + 2) + 2)/(1(3|x + 2| + 2) - 3))^2 + 1((2(3|x + 2| + 2) + 2)/(1(3|x + 2| + 2) - 3)) + 2)), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
For the function f(x) = 1cos(1π(2(-1(-1|x + 3| + 3))^2 - 4(-1(-1|x + 3| + 3))) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2sin(3π(-2(2|x + 1| + 1) + 5) - 1) positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|((-2(-1cos(1π(-3x^2 + 4x + 2) + 1)) + 1)/(-1(-1cos(1π(-3x^2 + 4x + 2) + 1)) - 3)) - 1| + 3 is strictly decreasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1((-1(-1sin(3π(4x + 1) - 3)))/(1(-1sin(3π(4x + 1) - 3)) + 3))^2 - 3 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|(1(2cos(3π(-2x^2 - 4x - 1) + 1) - 1) + 4)| - 1 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(2cos(2π(4x^2 + 3) + 3) + 2) + 3| + 1 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(4(-2|(-2cos(3πx - 2) + 3) + 3| + 3)^2 + 5(-2|(-2cos(3πx - 2) + 3) + 3| + 3) + 2) + 2 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3((-3(-1cos(3π(2|x - 1| - 3) - 3) - 2) + 2)/(3(-1cos(3π(2|x - 1| - 3) - 3) - 2) + 3))^2 - 5 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1((-1(3|(-2sin(2πx + 1) + 2)| + 3))/(2(3|(-2sin(2πx + 1) + 2)| + 3) + 1)) - 4 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 2((1(-3sin(1πx + 1) - 3) - 1)/(-1(-3sin(1πx + 1) - 3))) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1cos(1π(1|((-3(-1x^2 + 3) + 2)/(-1(-1x^2 + 3) + 2)) + 2| + 1) + 3) - 3 is strictly decreasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(1cos(2π(2x - 2) + 1) - 3) + 2| - 3 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(3π((-1(-1(-2|x - 1| + 1)) + 3)/(3(-1(-2|x - 1| + 1)) + 2))) + 3 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(3sin(2π(2x + 4) - 2) - 1) - 2| + 3 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(-1cos(3π(2|(-4x^2 + 1x - 4) - 2| - 1) - 3) - 2) - 1)/(-2(-1cos(3π(2|(-4x^2 + 1x - 4) - 2| - 1) - 3) - 2) - 3) positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|(1sin(2π(1(1x^2 + 3) - 5) - 2) + 3) - 3| is strictly increasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(2sin(2π((1x + 2)/(-2x - 1)) + 3) + 3) + 2| + 1 is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(3π((-3(1(-2x + 2)^2 - 5(-2x + 2) + 2) - 2)/(1(1(-2x + 2)^2 - 5(-2x + 2) + 2) + 3)) - 2) - 3 positive?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(-3sin(2π(-5x^2 + 1x)) - 3) - 2| - 1 is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(-3(-2sin(3π((2x + 1)/(-2x + 3)) + 3) + 3)^2 + 4(-2sin(3π((2x + 1)/(-2x + 3)) + 3) + 3)) - 2| - 1 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 2|(-5(5(1cos(1πx - 2) + 1) - 4)^2 + 2(5(1cos(1πx - 2) + 1) - 4) + 3) + 2| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 5(2sin(2π(1((-1x + 1)/(-1x))^2 - 2((-1x + 1)/(-1x)) - 3) + 1) - 1) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3|(-1sin(3π(-4x^2 + 1) + 3) - 1) - 2| - 1 is strictly decreasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3(-5(1|(1cos(2πx) + 2)| + 2) - 3) - 1)/(2(-5(1|(1cos(2πx) + 2)| + 2) - 3) - 3) negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(1(-2sin(2πx - 3) + 2)^2 + 5(-2sin(2πx - 3) + 2) - 3) negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -2|(2cos(2π(5((3x - 1)/(-2x + 1))^2 - 4((3x - 1)/(-2x + 1))) - 3) + 2) + 1| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(-2sin(1π(-2((-3x - 3)/(3x + 2))^2 + 3((-3x - 3)/(3x + 2)) + 4) - 1) - 1) + 2 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2sin(2π((-2(5(-1|x - 1| + 2)^2 - 4(-1|x - 1| + 2) + 2) - 1)/(1(5(-1|x - 1| + 2)^2 - 4(-1|x - 1| + 2) + 2) + 2)) - 3) - 1 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2sin(2π(-3(-1((-3x + 1)/(-1x))^2 + 5((-3x + 1)/(-1x)) + 4) + 1) - 3) - 1 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -2|(-4((-2(2cos(1πx - 1) - 1) - 2)/(-1(2cos(1πx - 1) - 1) + 2))^2 + 5((-2(2cos(1πx - 1) - 1) - 2)/(-1(2cos(1πx - 1) - 1) + 2)) - 4) + 2| + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 2sin(2π((2(-3(2|x + 2| - 3)^2 - 3(2|x + 2| - 3) - 5) + 2)/(-1(-3(2|x + 2| - 3)^2 - 3(2|x + 2| - 3) - 5) - 3)) - 3) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 3|(4(-2sin(3π(-3x + 3) + 3) - 1)^2 + 4(-2sin(3π(-3x + 3) + 3) - 1) - 2) - 2| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(2(1sin(1πx + 1) + 3) - 4) - 2| - 2 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(-1cos(3π(-5x^2 - 1) - 1) - 2) + 1 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 5(-2cos(3π((1x + 3)/(3x - 2)) - 1) - 1)^2 + 5(-2cos(3π((1x + 3)/(3x - 2)) - 1) - 1) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -4(-5(2sin(1πx - 2) - 1) - 4)^2 - 1(-5(2sin(1πx - 2) - 1) - 4) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1cos(3π(4(-4x - 5)^2 - 5(-4x - 5) - 5) + 1) - 1 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = (-1(3(3cos(3πx + 3) + 3) - 4) - 1)/(-3(3(3cos(3πx + 3) + 3) - 4) + 4), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -2(-3|((3(-1sin(3πx + 1) - 2))/(-2(-1sin(3πx + 1) - 2) - 3)) - 3| - 3) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2cos(2π(4(-1x - 1)^2 + 2(-1x - 1) - 5) - 2) + 1 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-3(2cos(2π(-3x - 2) - 1) - 2))/(-2(2cos(2π(-3x - 2) - 1) - 2) + 1) is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(-2sin(3π((-2(2x - 3) - 1)/(2(2x - 3) - 1)) - 2) - 2) - 2| - 3 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(2|((1(-2cos(1πx - 1) - 3) + 3)/(2(-2cos(1πx - 1) - 3) - 3)) - 1| + 1) positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = (-1(1sin(3π(-4(-5x + 5)^2 + 3) - 1) + 1) + 3)/(3(1sin(3π(-4(-5x + 5)^2 + 3) - 1) + 1) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-2(2|(-2cos(1π(1x^2 - 1x)) - 1) - 2| + 3) - 3)/(-2(2|(-2cos(1π(1x^2 - 1x)) - 1) - 2| + 3) + 3) positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(3sin(1π(1(-4x^2 + 5) + 1) + 2)) + 1| - 2 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3((1(-2sin(3πx + 3) + 3))/(-2(-2sin(3πx + 3) + 3) + 3)) + 3 is strictly increasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1cos(1π(4(-1|x + 2| - 2) - 3) + 2) + 2 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -5((3(-4(-1cos(2πx + 1) + 3)^2 + 4(-1cos(2πx + 1) + 3) - 4) + 3)/(-2(-4(-1cos(2πx + 1) + 3)^2 + 4(-1cos(2πx + 1) + 3) - 4) + 3)) + 4, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-2cos(2π((-2x - 1)/(-2x - 3)) - 2) + 2)^2 - 4(-2cos(2π((-2x - 1)/(-2x - 3)) - 2) + 2) + 1 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(-1|(-2sin(3π(-2x + 2) - 2)) - 3| - 3)^2 - 2(-1|(-2sin(3π(-2x + 2) - 2)) - 3| - 3) - 5 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3sin(1π(-5((2x + 2)/(2x)) - 5) + 1) + 2 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(-2|(4(2cos(3πx - 2) - 2)^2 - 3(2cos(3πx - 2) - 2) - 1) + 1|))/(3(-2|(4(2cos(3πx - 2) - 2)^2 - 3(2cos(3πx - 2) - 2) - 1) + 1|) + 2) positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(1cos(3π(2|(3x - 3) - 3| + 2) - 1) + 1)^2 + 2 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2((-1(-3|(-2sin(1πx + 2) + 3) + 1| - 3) - 2)/(2(-3|(-2sin(1πx + 2) + 3) + 1| - 3) + 1))^2 - 1((-1(-3|(-2sin(1πx + 2) + 3) + 1| - 3) - 2)/(2(-3|(-2sin(1πx + 2) + 3) + 1| - 3) + 1)) + 5 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = (-1(2cos(3π(-4(-1x - 3)^2 + 4(-1x - 3) - 4) + 1) + 1))/(3(2cos(3π(-4(-1x - 3)^2 + 4(-1x - 3) - 4) + 1) + 1) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(3cos(1π(3x + 5) - 3) + 3) - 1)/(2(3cos(1π(3x + 5) - 3) + 3) + 2) positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2cos(2π(1(1|x - 1| + 1)^2 - 5(1|x - 1| + 1) - 4) - 2) is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(5(-1cos(1πx + 1) + 2)) + 3| - 1 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -3sin(3π(-4(-3|((2x - 1)/(-1x + 2)) - 2|)^2 - 4(-3|((2x - 1)/(-1x + 2)) - 2|) - 2)) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3cos(2π(1(1x + 4)^2 + 3(1x + 4) + 4) - 3) + 3 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|((1(-1cos(3π(1x - 3) + 1) - 1) + 2)/(-1(-1cos(3π(1x - 3) + 1) - 1) - 3))| - 3 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -3sin(2π(-1|(5x^2 + 1x + 2) - 3| - 1) + 1) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(-1((-2(-1cos(2πx - 1) + 3) + 3)/(-3(-1cos(2πx - 1) + 3) - 2))^2 + 1((-2(-1cos(2πx - 1) + 3) + 3)/(-3(-1cos(2πx - 1) + 3) - 2)) + 5) + 2 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2sin(1π(-1|(-5x^2 - 3x - 5) - 2| - 3) + 1) - 1 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -2cos(3π(3|(4(-4x^2 - 5x + 2) + 4) + 2| - 2)), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(-3sin(1π(-3|x + 3| - 1)) + 2) - 3)/(-2(-3sin(1π(-3|x + 3| - 1)) + 2) + 1) is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -4((3(-3|(-2cos(2πx - 1) - 3) + 1| + 1) - 1)/(3(-3|(-2cos(2πx - 1) - 3) + 1| + 1)))^2 + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -1cos(3π((-3(2|(2x - 5)| + 1) - 1)/(1(2|(2x - 5)| + 1) - 3)) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 1|(3(2sin(3πx - 3) - 1) - 1) - 2| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -3|((2(-1cos(3πx + 1) + 1) - 2)/(3(-1cos(3πx + 1) + 1) - 1)) - 3| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3|(3sin(1π(1((-1x - 3)/(-2x - 3))^2 - 4((-1x - 3)/(-2x - 3))) - 1)) + 2| + 3 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 3((1(-3sin(3π(2|x| - 2)) - 3) - 3)/(-2(-3sin(3π(2|x| - 2)) - 3))), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -2sin(2π(-1|((-2x)/(-1x - 1))| + 3) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(-2sin(3π((-2(4x) - 2)/(-1(4x) - 3)) + 3) - 2)^2 - 3(-2sin(3π((-2(4x) - 2)/(-1(4x) - 3)) + 3) - 2) is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(-1cos(2π((-3(2x - 4) + 3)/(1(2x - 4))))) - 3| is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 2|(5(-3cos(3π(-3x - 5)) + 3)^2 - 4(-3cos(3π(-3x - 5)) + 3) + 2) - 3| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 1cos(3π(3(3|x - 3|)^2 - 3(3|x - 3|) + 3) + 2) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(-1cos(3π(1x^2 - 5) + 2) - 3) + 3)/(1(-1cos(3π(1x^2 - 5) + 2) - 3) - 2) positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -5(2|(5(3sin(3πx + 1))^2 + 1(3sin(3πx + 1)) - 1) + 2| + 3) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(3sin(1π(3|x|) - 3)) + 1 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2sin(2π(4(3x - 2)^2 + 1(3x - 2) - 2)) + 1 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 1|(2((-1(2cos(2πx - 1) - 3) + 3)/(-1(2cos(2πx - 1) - 3) + 2))^2 - 4((-1(2cos(2πx - 1) - 3) + 3)/(-1(2cos(2πx - 1) - 3) + 2)) + 1) - 2| + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2sin(1π(-2|(-3x^2 + 1x + 2)| + 1) - 3) - 3 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -1|(2(3(-3sin(1πx - 3))^2 - 5(-3sin(1πx - 3)) + 5) - 1)| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(-3(1sin(1π((2x + 2)/(-1x + 2)) - 1) + 1)^2 + 2(1sin(1π((2x + 2)/(-1x + 2)) - 1) + 1) - 5) - 2 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3(1|(-2cos(3πx + 1) + 3) + 2| - 2) + 1)/(-1(1|(-2cos(3πx + 1) + 3) + 2| - 2) + 2) positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 2cos(3π(2|((-2x)/(3x + 2)) - 3| + 2) - 3) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(-5(-3(3cos(1πx - 2) - 1)^2 + 4) - 2) + 1)/(-2(-5(-3(3cos(1πx - 2) - 1)^2 + 4) - 2) + 1) is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 2|(3sin(2π((1x + 3)/(2x - 1)) - 3) + 2) - 3| + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 3(-1sin(2π(-2|((2x)/(1x + 1)) - 1| - 2) - 1) - 3) + 4, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(1(1sin(1π((-2x - 1)/(-1x + 3)) + 2) - 2)^2 - 1(1sin(1π((-2x - 1)/(-1x + 3)) + 2) - 2) - 2) - 3 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = (-2(-3|(-2cos(2π(4x + 1)) - 1) + 1| - 3))/(-1(-3|(-2cos(2π(4x + 1)) - 1) + 1| - 3) - 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1sin(1π(-1((1(2x - 3) + 2)/(1(2x - 3)))^2 + 4) + 1) + 2 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 1((2(3sin(2π(1|x + 3| - 3) - 3) + 2) - 1)/(2(3sin(2π(1|x + 3| - 3) - 3) + 2) + 1)) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(-1(-2sin(3πx + 3) + 1)^2 + 1(-2sin(3πx + 3) + 1) + 5) + 3| - 1 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(-1(1sin(3πx - 1) + 2) + 3) - 1| - 1 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (3(3|(3sin(1π(4x + 1)) - 3) - 1|) + 3)/(-3(3|(3sin(1π(4x + 1)) - 3) - 1|)) is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(1sin(1π(3x - 1) + 3)) - 1| is strictly decreasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(3|(3sin(3πx + 1) - 3) + 2| - 3) - 1 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(-2sin(1π(4x + 1) - 2) - 3) + 1| is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(1π((2(3(-3|x + 3| + 1)^2 + 4(-3|x + 3| + 1) - 1) + 1)/(3(3(-3|x + 3| + 1)^2 + 4(-3|x + 3| + 1) - 1) - 2)) + 2) positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5((-1(2sin(3πx + 3) - 3))/(1(2sin(3πx + 3) - 3) + 1)) - 3 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1cos(2π(4(-4((-3x + 3)/(3x - 1))^2 + 3((-3x + 3)/(3x - 1)) - 1) + 2) - 1) - 1 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(-2|(-1cos(1πx + 3) - 2) + 2| - 3) + 4 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(-5(-3sin(1πx - 2) - 1)^2 + 5(-3sin(1πx - 2) - 1) - 4) - 2| - 2 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 1|(-3cos(1π(2x + 4) - 1))|, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(-2cos(2π((-1x + 2)/(-2x)) - 3) - 3) - 1 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2sin(1π(-2|(4(5x^2 + 1x - 2) - 3) + 3|) - 3) is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|(2(3cos(1π(-4x - 3) - 3) - 3)^2 + 3) - 3| + 2 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 5((3(-1sin(3πx - 1) - 2) + 3)/(-1(-1sin(3πx - 1) - 2) - 3))^2 + 5((3(-1sin(3πx - 1) - 2) + 3)/(-1(-1sin(3πx - 1) - 2) - 3)) - 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(1cos(2π(-3((3x)/(-2x - 3)) - 4) + 1) + 2)^2 + 5 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(-1sin(1π(4((3x + 1)/(2x - 1))^2 + 4((3x + 1)/(2x - 1)) + 3)) + 3) + 3| - 2 is strictly increasing.

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[User]
For the function f(x) = -3(-1sin(3π(-3|(-1x^2 + 1x - 2) + 3| - 3) + 2) + 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
For the function f(x) = (-2(3(2|(-1cos(3πx + 3) + 2) + 1| + 2) - 1) - 3)/(2(3(2|(-1cos(3πx + 3) + 2) + 1| + 2) - 1) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2cos(1π(2|(1(-5x + 5)^2 - 1(-5x + 5) + 2) - 2|) - 2) - 1 is strictly decreasing.

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[User]
For the function f(x) = (1(1cos(3π(1(2|x + 2| - 2) - 2) + 2) + 3) - 2)/(3(1cos(3π(1(2|x + 2| - 2) - 2) + 2) + 3) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
For the function f(x) = (-1(-3|(2sin(1π(-4x^2 - 3x - 2) - 3) - 2)| + 2) + 2)/(-2(-3|(2sin(1π(-4x^2 - 3x - 2) - 3) - 2)| + 2) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2cos(3π(3|(-4(4x^2 - 5x - 5) - 4) + 3| + 1) - 3) negative?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3|(1sin(3π(-2x^2 + 2x + 4) - 1) + 2) + 3| is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(-2(2sin(3π(3|x - 2| - 2) - 2) - 1)^2 + 5(2sin(3π(3|x - 2| - 2) - 2) - 1) - 2) + 1)/(-1(-2(2sin(3π(3|x - 2| - 2) - 2) - 1)^2 + 5(2sin(3π(3|x - 2| - 2) - 2) - 1) - 2) - 2) positive?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-3(1cos(1π(4(-3|x - 2|) - 2) + 1)) - 2)/(-1(1cos(1π(4(-3|x - 2|) - 2) + 1)) + 2) is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(-3sin(3π(5(2|x + 2|) - 2) + 3) - 3) - 2)/(1(-3sin(3π(5(2|x + 2|) - 2) + 3) - 3) + 1) negative?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5((-3(1cos(3πx - 2) + 2) - 2)/(-2(1cos(3πx - 2) + 2))) - 4 is strictly increasing.

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[User]
For the function f(x) = -1((3(-2cos(1π(-3|x - 2| + 3) - 3) + 1) - 3)/(-1(-2cos(1π(-3|x - 2| + 3) - 3) + 1) - 2))^2 + 1((3(-2cos(1π(-3|x - 2| + 3) - 3) + 1) - 3)/(-1(-2cos(1π(-3|x - 2| + 3) - 3) + 1) - 2)), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1cos(3π(3(-2|x - 2| + 1) - 1) - 2) - 2 positive?

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[User]
For the function f(x) = 2(-2sin(3π(1|(-5x - 1) + 2| + 2)) + 1)^2 + 4(-2sin(3π(1|(-5x - 1) + 2| + 2)) + 1) + 4, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|(-3(2(3cos(2πx + 2) - 1)^2 - 1(3cos(2πx + 2) - 1)) - 5)| - 1 negative?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1((-2(-3cos(1π(1x^2 - 3x - 4) - 3) - 2) - 1)/(-1(-3cos(1π(1x^2 - 3x - 4) - 3) - 2) + 3)) - 1 is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|(4(1cos(1πx - 2) + 1)) + 1| - 2 negative?

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[User]
For the function f(x) = -3sin(2π(2((3x + 3)/(-2x - 3))^2 - 2((3x + 3)/(-2x - 3)) + 1) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
For the function f(x) = (1(-1sin(1π(-1|x - 3| - 1) - 1)) - 2)/(1(-1sin(1π(-1|x - 3| - 1) - 1)) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3cos(1π(-4(-1|((1x + 2)/(2x))| + 3)^2 + 5(-1|((1x + 2)/(2x))| + 3) + 4) - 1) + 3 negative?

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[User]
For the function f(x) = 2((1(-2|(3cos(3πx + 1) - 3) - 1| + 3) - 2)/(-2(-2|(3cos(3πx + 1) - 3) - 1| + 3) + 3)) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(1sin(2π((2x - 1)/(-1x + 2)) - 2) - 2) + 1 is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3((2(1cos(1πx + 3)))/(-2(1cos(1πx + 3)) - 1))^2 + 4((2(1cos(1πx + 3)))/(-2(1cos(1πx + 3)) - 1)) - 4 positive?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1sin(1π(-3(-3(-2|x + 3| + 2) + 4)^2 + 5(-3(-2|x + 3| + 2) + 4) + 2) - 3) - 2 is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2(5(-2sin(3πx + 2) - 1) - 1)^2 + 3(5(-2sin(3πx + 2) - 1) - 1) + 4 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = (2(5(2cos(1πx - 2) - 2)^2 - 3(2cos(1πx - 2) - 2) - 5) + 3)/(-2(5(2cos(1πx - 2) - 2)^2 - 3(2cos(1πx - 2) - 2) - 5) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
For the function f(x) = -1(1|(2cos(2πx - 3) - 3) + 3| + 1)^2 - 1(1|(2cos(2πx - 3) - 3) + 3| + 1) - 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(2sin(2π(-1|(4x^2 - 2x - 5)| - 3) - 1) + 3) + 1 positive?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2((1(2(-1cos(2πx - 3) + 3)^2 - 1(-1cos(2πx - 3) + 3) - 5))/(-3(2(-1cos(2πx - 3) + 3)^2 - 1(-1cos(2πx - 3) + 3) - 5) - 2)) + 4 is strictly decreasing.

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[User]
For the function f(x) = -3|(3(-3cos(2π(-3x + 1) - 2) - 3)^2 - 5(-3cos(2π(-3x + 1) - 2) - 3) + 5) - 2| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -4(2(-3sin(2π((-1x + 1)/(3x + 2)) - 3) - 3)^2 + 1(-3sin(2π((-1x + 1)/(3x + 2)) - 3) - 3) - 1) + 4 positive?

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(-5(2cos(2π((-3x + 3)/(2x + 3))) - 2)^2 + 3(2cos(2π((-3x + 3)/(2x + 3))) - 2) + 3) - 3| + 2 negative?

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3((-3(2|(-2cos(1πx))| - 2) + 2)/(-1(2|(-2cos(1πx))| - 2) + 3)) + 3 negative?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(4(5(3cos(1πx - 2) - 2) - 2)^2 + 1(5(3cos(1πx - 2) - 2) - 2)) + 3)/(1(4(5(3cos(1πx - 2) - 2) - 2)^2 + 1(5(3cos(1πx - 2) - 2) - 2)) - 3) is strictly increasing.

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[User]
For the function f(x) = 3sin(1π((3(2|x - 2| - 2))/(-1(2|x - 2| - 2) + 2)) - 2) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(3sin(3π((1x)/(-1x - 3)) + 2) + 3)^2 + 4 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(1sin(2π(3(5x - 5)^2 - 1(5x - 5) - 2)) - 3) + 3| - 3 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(3|(1cos(1πx + 2) - 3)| - 3) + 2 is strictly decreasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(3π(-3|((-1x + 3)/(-2x + 1)) - 1|) + 3) negative?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(3(1(1cos(2πx))^2 + 4(1cos(2πx)) - 3) - 5) + 2| - 3 is strictly decreasing.

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[User]
For the function f(x) = -4((-2(3cos(1πx - 3)) + 3)/(2(3cos(1πx - 3)) - 1)) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|(2sin(3π((-1x + 1)/(2x)) + 1) + 1) - 1| + 2 is strictly increasing.

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[User]
For the function f(x) = -1(-2|(2sin(1πx - 1) - 1) + 1| - 3) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3cos(2π(-2(1x^2 + 2x) - 5) - 1) + 1 is strictly decreasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(-3(2sin(2π(2|x - 3| - 3) + 2) + 2)^2 - 5(2sin(2π(2|x - 3| - 3) + 2) + 2) + 5) + 2)/(-1(-3(2sin(2π(2|x - 3| - 3) + 2) + 2)^2 - 5(2sin(2π(2|x - 3| - 3) + 2) + 2) + 5) + 3) is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(1sin(3π(-3((1x - 2)/(2x - 1)) - 1) - 2)) - 2| - 1 is strictly increasing.

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[User]
For the function f(x) = -1|((2(1(1sin(3πx + 2) + 2) - 1) - 3)/(-3(1(1sin(3πx + 2) + 2) - 1) - 1)) - 3| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2cos(3π(-5(1x + 1)^2 + 2(1x + 1) - 4) - 2) - 2 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 2|(1(2sin(1πx) - 1)^2 - 5(2sin(1πx) - 1) + 3) - 1| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2sin(1π(3|((1x - 2)/(3x - 1)) + 3|)) negative?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-1|(2sin(1πx) + 1) - 3| + 3) + 3 is strictly increasing.

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[User]
For the function f(x) = -1cos(2π(-4(-4x^2 + 5x + 4) + 2) - 3) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3cos(2π(-3|(-4x^2 - 5x + 1) - 1| - 2)) + 2 is strictly decreasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(3cos(2π(2|(4x + 2) + 1| - 1) - 3) + 2)^2 + 4(3cos(2π(2|(4x + 2) + 1| - 1) - 3) + 2) + 2 is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|(-3cos(3π(5(-4x^2 - 1x - 2) + 1) + 3) - 1) + 3| - 2 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 3(-3sin(1π(1|x + 2| - 2) + 1) - 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(1(1cos(3πx - 1) - 2) + 2)^2 + 3(1(1cos(3πx - 1) - 2) + 2) - 5 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 5(1(1|(-1sin(3πx - 1) + 1) - 1| + 3) + 4)^2 - 2(1(1|(-1sin(3πx - 1) + 1) - 1| + 3) + 4) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(1cos(2π(-3(2|x + 2|) - 1) + 3) - 1) + 3)/(1(1cos(2π(-3(2|x + 2|) - 1) + 3) - 1)) negative?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(3|(3cos(3πx + 3) + 2) + 1| + 2) - 1)/(-3(3|(3cos(3πx + 3) + 2) + 1| + 2) + 1) is strictly decreasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3sin(1π(3|(-4(-2x^2 + 2x) + 2) + 2| + 3)) is strictly increasing.

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[User]
For the function f(x) = -1sin(2π((-2(-3(-2|x + 3|) - 4) + 1)/(-1(-3(-2|x + 3|) - 4))) + 2) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2sin(1π(-4(-1|(3x - 4) - 1| - 2)^2 - 3(-1|(3x - 4) - 1| - 2) + 4) + 1) - 2 positive?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2((-2(3sin(3π(3|x - 3| - 1) - 1) + 3) - 2)/(-3(3sin(3π(3|x - 3| - 1) - 1) + 3) - 2))^2 - 3((-2(3sin(3π(3|x - 3| - 1) - 1) + 3) - 2)/(-3(3sin(3π(3|x - 3| - 1) - 1) + 3) - 2)) - 1 is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(2sin(3π(1x + 4) + 2) - 2) + 1| + 2 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 2|(2(3sin(2π(2x^2 + 5x + 3) - 1)) + 2) - 1| + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(-1(-2|(-1sin(1πx + 1) + 2) + 3|) + 4) - 1)/(-1(-1(-2|(-1sin(1πx + 1) + 2) + 3|) + 4)) positive?

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[User]
For the function f(x) = 3((-3(1sin(1πx - 2)) - 1)/(2(1sin(1πx - 2)) + 2))^2 + 1((-3(1sin(1πx - 2)) - 1)/(2(1sin(1πx - 2)) + 2)) - 4, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -2cos(3π(-2(2|(5x^2 + 5) - 2| + 3) - 2) + 1) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4((-1(3cos(3πx) - 3) + 2)/(2(3cos(3πx) - 3) - 1)) + 1 is strictly increasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3sin(1π(1(-2|(-3x + 4) - 1|)^2 - 3(-2|(-3x + 4) - 1|) + 3) + 1) is strictly decreasing.

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[User]
For the function f(x) = -1|(-3(2sin(2π(2x^2 + 2x + 2) - 2) - 2) - 4) + 2| + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
For the function f(x) = -3sin(1π(-4(2|x| - 3)) + 3) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-1sin(3π((1x + 3)/(2x + 1)) - 1) + 1) is strictly increasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(-3cos(3π(-3|((-3x - 3)/(-1x + 3)) - 3| - 2) - 2) + 2)^2 - 4(-3cos(3π(-3|((-3x - 3)/(-1x + 3)) - 3| - 2) - 2) + 2) - 4 is strictly increasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 5(-2|(-4(2cos(1πx) - 2)^2 - 2(2cos(1πx) - 2) + 3) + 2| + 1) - 2 is strictly decreasing.

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[User]
For the function f(x) = 1|((3(-3sin(2π(5x + 4) + 3) + 2) - 3)/(-2(-3sin(2π(5x + 4) + 3) + 2) + 3))| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 3cos(1π(-1(-3x^2 - 5x - 3) - 1)) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(-2(-4(-3sin(2πx + 2) - 2) + 3)^2 + 3(-4(-3sin(2πx + 2) - 2) + 3) - 3) + 3)/(-1(-2(-4(-3sin(2πx + 2) - 2) + 3)^2 + 3(-4(-3sin(2πx + 2) - 2) + 3) - 3) + 2) negative?

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[User]
For the function f(x) = 2((1(2sin(1πx + 1)))/(2(2sin(1πx + 1)) - 1)) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = (-2(3|(-2sin(3πx - 2) - 2)| + 1) - 3)/(2(3|(-2sin(3πx - 2) - 2)| + 1)), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(3cos(2π(2|((-1x - 2)/(-2x - 3)) + 3| - 2) + 1) + 3) + 2 is strictly increasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(3sin(2π(-1|x - 2| + 3) + 3))^2 + 4(3sin(2π(-1|x - 2| + 3) + 3)) + 1 is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1sin(3π(-1(5(3|x + 3| + 1)^2 + 1(3|x + 3| + 1) + 1) - 3) + 2) - 2 positive?

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[User]
For the function f(x) = 1|(-1sin(2π(3x + 4) + 1) - 2) + 3| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(-1sin(1π(1((3x - 1)/(2x - 3))^2 + 5((3x - 1)/(2x - 3))) - 2) - 1) - 1 is strictly increasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(-1|(3sin(2πx + 2)) + 1| - 3) - 2 is strictly increasing.

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[User]
For the function f(x) = (1(2|(3sin(2πx + 1) - 3) + 1| - 3) + 1)/(-1(2|(3sin(2πx + 1) - 3) + 1| - 3) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(-3|(3cos(1πx - 2) - 1)|))/(1(-3|(3cos(1πx - 2) - 1)|) + 2) is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1sin(2π(2(-3|((3x)/(-3x - 3)) - 1|) + 3) - 2) - 1 positive?

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2(3cos(2π(3x - 3) - 3))^2 + 1(3cos(2π(3x - 3) - 3)) - 4 negative?

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[User]
For the function f(x) = -2|(4(-1sin(1πx + 3) + 3) + 5)| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2(-3cos(2π(-1x^2 - 4x + 3) + 3) + 2) + 1)/(-3(-3cos(2π(-1x^2 - 4x + 3) + 3) + 2) + 2) is strictly increasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(2cos(3π(-1x^2 - 1x - 1) - 2) - 1) + 3 is strictly decreasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-2(-3|(2(1sin(3πx + 1) - 2) - 2) - 3| - 2) - 3)/(3(-3|(2(1sin(3πx + 1) - 2) - 2) - 3| - 2) - 1) negative?

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[User]
For the function f(x) = -4(-5(-1|(1cos(2πx) - 2) - 1| + 3)^2 + 1(-1|(1cos(2πx) - 2) - 1| + 3) - 2) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2cos(3π(1(3|x - 3| - 3)^2 - 1(3|x - 3| - 3) + 3) + 3) + 1 is strictly decreasing.

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[User]
For the function f(x) = -5((-2(3cos(3πx - 3) + 2) - 2)/(-1(3cos(3πx - 3) + 2))), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(2sin(2π(-2|x - 2| + 2) + 3) - 3) - 3)/(-3(2sin(2π(-2|x - 2| + 2) + 3) - 3) - 3) positive?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1sin(1π(1|(-1x^2 + 3x + 1) - 3| + 2) - 1) + 1 is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(2π(3|(1x^2 + 5x) - 2| - 2)) - 3 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(1|(1cos(2πx - 1) + 1) - 2| + 2)^2 - 5 is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1cos(2π((-2(-2|x - 2| + 1) - 1)/(-1(-2|x - 2| + 1)))) - 3 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3cos(1π(-2|(-2(5x^2 - 4x - 3) - 5)| + 2) - 1) positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 5(1|(5(-1sin(3πx) - 1)^2 - 2(-1sin(3πx) - 1)) + 3| + 3) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(1cos(3π(4(1x - 1)^2 + 4(1x - 1)) - 3) - 1) - 1)/(-2(1cos(3π(4(1x - 1)^2 + 4(1x - 1)) - 3) - 1) + 1) negative?

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[User]
For the function f(x) = -1cos(1π(-5((3x)/(1x - 3))^2 - 4((3x)/(1x - 3)) + 3) + 3) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
For the function f(x) = 3|((-1(1cos(3π(-2x + 1) - 3) + 3) - 2)/(1(1cos(3π(-2x + 1) - 3) + 3) + 1)) - 1| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-3(-1(-1(-3cos(3πx - 1) + 1) - 4)^2 + 4(-1(-3cos(3πx - 1) + 1) - 4) - 1) - 1)/(-3(-1(-1(-3cos(3πx - 1) + 1) - 4)^2 + 4(-1(-3cos(3πx - 1) + 1) - 4) - 1) - 3) is strictly decreasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3sin(1π(4(1x + 1)^2 - 1(1x + 1) + 3) + 2) positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -3sin(2π(2(2|x - 3| + 3)^2 - 3(2|x - 3| + 3) - 2) - 1) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 4(1cos(3π(1|x - 2| + 2) + 3) + 2)^2 + 2(1cos(3π(1|x - 2| + 2) + 3) + 2) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4((-2(4(1cos(1πx + 1) + 3) - 1) - 3)/(-1(4(1cos(1πx + 1) + 3) - 1)))^2 + 5((-2(4(1cos(1πx + 1) + 3) - 1) - 3)/(-1(4(1cos(1πx + 1) + 3) - 1))) + 4 is strictly decreasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(2cos(1π((1x + 2)/(-1x - 3)) - 3) + 2) - 1 is strictly increasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4((-2(4(2sin(1πx) - 2) - 4) - 3)/(-1(4(2sin(1πx) - 2) - 4) + 2))^2 + 4((-2(4(2sin(1πx) - 2) - 4) - 3)/(-1(4(2sin(1πx) - 2) - 4) + 2)) - 2 is strictly decreasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3cos(3π((1(2|x - 3| - 1) + 2)/(2(2|x - 3| - 1) - 3)) + 2) + 2 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 1(-1sin(1π(1x^2 + 5x + 3) - 1) + 1) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -5(2cos(1π(5(-3|x + 2| + 2) - 3) - 1))^2 - 3(2cos(1π(5(-3|x + 2| + 2) - 3) - 1)) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -3cos(1π(-1(-1|(4x - 2) - 2|)^2 + 3) + 1) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 1(1cos(3π(-2(3|x - 1| - 2) + 4) + 1))^2 + 2(1cos(3π(-2(3|x - 1| - 2) + 4) + 1)) + 4, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(3cos(1π(3x^2 - 3x - 1)) - 2) + 2 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2cos(3π(-1|(-1x^2 + 5x + 3) + 3| + 3)) - 3 is strictly increasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1sin(2π(-3|((-3x - 3)/(1x)) + 1| - 1) + 3) - 3 is strictly decreasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -1cos(3π(3|(4x^2 + 2x) + 3| - 2) - 1) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 2(-2cos(2π(-1|x - 1|) - 2) - 3) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
For the function f(x) = 1cos(3π(-4(-3|x + 2| + 2) + 3) + 1) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2((-3(-2(2cos(1πx - 3) + 2)^2 - 3(2cos(1πx - 3) + 2) - 5) + 1)/(2(-2(2cos(1πx - 3) + 2)^2 - 3(2cos(1πx - 3) + 2) - 5) + 3)) + 1 is strictly decreasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(5(3sin(3π(2|x + 3| + 2) + 3) - 1) + 4)^2 + 4(5(3sin(3π(2|x + 3| + 2) + 3) - 1) + 4) + 1 positive?

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(1|(-1(-2cos(2πx) + 3)^2 - 5(-2cos(2πx) + 3) - 3)| - 3) - 2)/(-2(1|(-1(-2cos(2πx) + 3)^2 - 5(-2cos(2πx) + 3) - 3)| - 3) - 1) positive?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(3cos(3π(-4x + 5) + 1) - 1)^2 - 5(3cos(3π(-4x + 5) + 1) - 1) + 1 is strictly increasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2(-2sin(1π((-1x - 1)/(1x)) + 1) + 1)^2 - 3(-2sin(1π((-1x - 1)/(1x)) + 1) + 1) - 4 is strictly increasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(-1(2sin(3πx + 3) + 1)^2 - 5(2sin(3πx + 3) + 1) + 1) - 3| - 2 is strictly increasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(-1(1sin(3πx - 2) - 3)^2 + 4(1sin(3πx - 2) - 3) + 1) - 2)/(2(-1(1sin(3πx - 2) - 3)^2 + 4(1sin(3πx - 2) - 3) + 1) + 3) is strictly increasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(-2(1sin(1πx + 1) + 3) - 2)^2 + 4(-2(1sin(1πx + 1) + 3) - 2) - 2 is strictly decreasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(5(2sin(1π(1|x - 2| - 1)) - 2) - 4))/(-1(5(2sin(1π(1|x - 2| - 1)) - 2) - 4) + 2) positive?

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[User]
For the function f(x) = (1(3sin(1π(3|x + 1| - 1) + 2) - 2) - 2)/(3(3sin(1π(3|x + 1| - 1) + 2) - 2) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1cos(1π(-3((3(-3x - 2) + 3)/(-1(-3x - 2) + 3))^2 - 2((3(-3x - 2) + 3)/(-1(-3x - 2) + 3)) - 3) + 3) is strictly decreasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2sin(2π(-3|(-2(-3x - 2)^2 - 4(-3x - 2) - 3) + 3| + 3) + 3) + 1 positive?

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[User]
For the function f(x) = -3(-3|((-1(-1sin(3πx - 2) + 3) + 3)/(-3(-1sin(3πx - 2) + 3) + 1)) + 1|) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
For the function f(x) = 2cos(3π((-3(-4x^2 + 3x - 1) - 1)/(-3(-4x^2 + 3x - 1) - 2)) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3sin(3π(4(-1x^2 + 4x + 3) - 5) - 3) - 2 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 1sin(2π((2(-1x - 3) - 2)/(3(-1x - 3) + 3)) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
For the function f(x) = (3(-3|(3sin(2πx) - 3) + 2| + 1) + 3)/(3(-3|(3sin(2πx) - 3) + 2| + 1) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
For the function f(x) = (2(-1(-2sin(2πx + 1) - 3)^2 - 1(-2sin(2πx + 1) - 3) - 5) + 2)/(-2(-1(-2sin(2πx + 1) - 3)^2 - 1(-2sin(2πx + 1) - 3) - 5) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 4((2(2cos(3πx - 3)) - 2)/(-1(2cos(3πx - 3)) + 3))^2 + 4((2(2cos(3πx - 3)) - 2)/(-1(2cos(3πx - 3)) + 3)) - 3 negative?

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3sin(1π(-3|(1x^2 - 4x + 3) + 2| + 2) - 2) + 1 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -4(1cos(3π(-4x^2 + 5x + 1) - 2) - 1) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(-3cos(2π((2x)/(2x - 1)) + 3) - 1)^2 + 1(-3cos(2π((2x)/(2x - 1)) + 3) - 1) - 4 is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(-1sin(1π(1|(-1x^2 + 5x - 1) + 2| + 1) - 2) + 3) - 1)/(-1(-1sin(1π(1|(-1x^2 + 5x - 1) + 2| + 1) - 2) + 3) - 1) positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 2|(2cos(2π(-3x^2 - 1) - 2) - 2) + 2| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
For the function f(x) = -1|(3(2(3cos(1πx - 3) - 3)^2 + 2(3cos(1πx - 3) - 3) - 5) + 3) + 1| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(1(2|(3sin(3πx - 2) - 3) + 1| + 1)^2 + 3(2|(3sin(3πx - 2) - 3) + 1| + 1) - 5) + 2)/(1(1(2|(3sin(3πx - 2) - 3) + 1| + 1)^2 + 3(2|(3sin(3πx - 2) - 3) + 1| + 1) - 5)) positive?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1sin(1π(-1|(5((3x + 3)/(-3x - 2))^2 - 2((3x + 3)/(-3x - 2)) + 3) + 3|) - 3) - 1 is strictly decreasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|((1(-3cos(1π(2x + 3) + 2) - 2) + 1)/(-1(-3cos(1π(2x + 3) + 2) - 2) - 2)) - 3| is strictly decreasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(5(-2sin(1π(-2|x + 1| + 2) - 1) + 3)^2 + 2(-2sin(1π(-2|x + 1| + 2) - 1) + 3) - 5) - 5 is strictly decreasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(3|(2cos(2π(-4x + 3) - 1) - 1)| - 3)^2 + 2(3|(2cos(2π(-4x + 3) - 1) - 1)| - 3) is strictly increasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3cos(1π(2|((3x + 2)/(-2x + 1)) - 3| - 2) + 2) - 2 is strictly decreasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2(5(2sin(2π(-1x^2 + 4x) + 2)) - 4) - 3)/(-1(5(2sin(2π(-1x^2 + 4x) + 2)) - 4) - 3) is strictly increasing.

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[User]
For the function f(x) = 3sin(1π(-4(2|x| - 1)^2 - 4(2|x| - 1) - 5) - 3) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
For the function f(x) = -2cos(2π(3((-2x + 3)/(2x + 1))^2 - 2((-2x + 3)/(2x + 1)))), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2sin(2π(-1|(3(1x - 5)^2 + 3(1x - 5) + 1) + 3| - 2) - 2) + 1 is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(2|(3(-1cos(1πx - 1)) + 4) - 3| + 1) + 2)/(1(2|(3(-1cos(1πx - 1)) + 4) - 3| + 1)) negative?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-1|(2cos(1πx - 2) - 1) - 1| + 1) - 5 is strictly increasing.

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[User]
For the function f(x) = (-3(-2(-1sin(2πx - 3) - 1)^2 + 4(-1sin(2πx - 3) - 1) + 4) - 1)/(-1(-2(-1sin(2πx - 3) - 1)^2 + 4(-1sin(2πx - 3) - 1) + 4) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4((3(-1|(-2sin(1πx + 1))| - 2))/(-1(-1|(-2sin(1πx + 1))| - 2) + 2)) - 5 is strictly increasing.

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[User]
For the function f(x) = -3sin(3π((-1(1(2|x + 3| + 1) - 2) - 3)/(-3(1(2|x + 3| + 1) - 2) + 1))) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(3sin(1π(-3x + 4)) + 1) + 3)/(-2(3sin(1π(-3x + 4)) + 1) - 3) is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3(1|(3sin(3πx - 2) + 1) + 3| + 2) + 3)/(-1(1|(3sin(3πx - 2) + 1) + 3| + 2) - 1) negative?

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[User]
For the function f(x) = (-1(2(2sin(3π(-5x^2 + 3x + 3) - 2) - 2)) + 2)/(1(2(2sin(3π(-5x^2 + 3x + 3) - 2) - 2))), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(-2(-1cos(3π(2x^2) - 3) + 1) + 1) + 3)/(-2(-2(-1cos(3π(2x^2) - 3) + 1) + 1)) is strictly decreasing.

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[User]
For the function f(x) = -3((-1(-1sin(3πx + 2) + 1) + 3)/(1(-1sin(3πx + 2) + 1) + 3))^2 - 4((-1(-1sin(3πx + 2) + 1) + 3)/(1(-1sin(3πx + 2) + 1) + 3)) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(1(-1cos(2πx + 1) + 1)^2 - 2(-1cos(2πx + 1) + 1) - 4) positive?

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(5(3sin(3π(-2|x| - 2)) + 1) - 1)^2 - 4(5(3sin(3π(-2|x| - 2)) + 1) - 1) + 1 negative?

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1((3(3sin(1πx - 2) + 3))/(-2(3sin(1πx - 2) + 3) + 3)) - 1 negative?

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(4(-3cos(3π((-2x - 3)/(-1x - 2)) + 2) - 2)^2 - 3(-3cos(3π((-2x - 3)/(-1x - 2)) + 2) - 2) + 5) + 2| - 2 negative?

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(-2cos(2π(2x - 2) - 1)) - 3| negative?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2sin(1π(3|(-4x + 3) - 3| - 2) + 3) - 3 is strictly decreasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2sin(1π((2(-3|x - 1| + 1) + 1)/(3(-3|x - 1| + 1) + 3)) + 2) + 3 is strictly decreasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(2cos(3π(4(1x^2 + 2x - 4) + 1) + 3) + 1) - 1| positive?

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[User]
For the function f(x) = -4((-1(2sin(3πx) + 3) + 3)/(-3(2sin(3πx) + 3) + 4)) + 4, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
For the function f(x) = -1sin(1π(3|(-1x^2 - 5x + 3) - 1| - 3) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2(-1cos(1π(1x + 2) + 2) - 2) - 1)/(2(-1cos(1π(1x + 2) + 2) - 2) + 2) is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(3|(-1cos(1π(2x - 5)) + 2) - 2| - 2)^2 - 3(3|(-1cos(1π(2x - 5)) + 2) - 2| - 2) + 2 positive?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(1(3sin(3π(-1|x + 2| + 1) + 1) - 2) - 1)^2 + 4(1(3sin(3π(-1|x + 2| + 1) + 1) - 2) - 1) - 1 is strictly increasing.

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[User]
For the function f(x) = -2|(5(-2cos(3πx) + 3) - 2) + 2| + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(1(-2sin(3πx - 2) - 2) + 4) - 2| + 1 negative?

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3(1cos(3π((-2x - 1)/(-1x)) - 3) - 1)^2 - 4(1cos(3π((-2x - 1)/(-1x)) - 3) - 1) - 5 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = (-1(2(-3(-3cos(1πx - 1) - 1)^2 - 1(-3cos(1πx - 1) - 1) + 5) - 1) - 2)/(-2(2(-3(-3cos(1πx - 1) - 1)^2 - 1(-3cos(1πx - 1) - 1) + 5) - 1) - 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(2π(-5(-1x^2 + 2x + 4) - 4) + 3) + 1 negative?

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[User]
For the function f(x) = -4(-1(1cos(2πx - 3) - 1))^2 + 2(-1(1cos(2πx - 3) - 1)) - 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
For the function f(x) = 1(2|(2cos(3πx - 2) + 1)| - 2)^2 + 3(2|(2cos(3πx - 2) + 1)| - 2) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
For the function f(x) = 1sin(3π((-3(1x^2 + 2x + 4) - 1)/(-1(1x^2 + 2x + 4) + 2)) - 3) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(-3cos(2π(4((-2x + 1)/(-1x - 1))^2 - 5((-2x + 1)/(-1x - 1)) + 4) + 3) - 2) + 5 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -2|(-3sin(1π(-1x + 1) + 1) - 2)| + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
For the function f(x) = -2|((-3(-3(1cos(1πx + 3) - 3)^2 + 1(1cos(1πx + 3) - 3)) - 2)/(-1(-3(1cos(1πx + 3) - 3)^2 + 1(1cos(1πx + 3) - 3)) - 3)) + 2| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 1(4(-2sin(2πx - 2) + 1) - 1)^2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = (1(1|(5(-1cos(1πx - 2) - 2) + 3) - 1| + 1) + 3)/(-2(1|(5(-1cos(1πx - 2) - 2) + 3) - 1| + 1)), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -1|((2(-3(3sin(2πx - 1)) - 2))/(-1(-3(3sin(2πx - 1)) - 2) + 2)) - 2| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
For the function f(x) = -1|(2cos(2π(2x^2 - 5x - 5) + 1) + 2) + 1| + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(2sin(3π(-2|x + 2| + 2)) + 2) + 4 is strictly increasing.

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[User]
For the function f(x) = (-3(1sin(3π(1|x - 2| + 3) + 1) + 2) - 2)/(-2(1sin(3π(1|x - 2| + 3) + 1) + 2) - 3), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(2(1sin(3πx + 1) - 1) - 1)^2 - 2(2(1sin(3πx + 1) - 1) - 1) + 1 is strictly decreasing.

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[User]
For the function f(x) = -3cos(2π((-1(-2x + 1) + 2)/(1(-2x + 1) + 2)) - 1) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1cos(1π(1|(-5x^2 + 5x - 5) - 1| + 1) - 1) + 2 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -2|(1(-3sin(1πx - 3) - 3)) + 3| + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(1(-2sin(1πx - 2) - 3) + 4)^2 + 3(1(-2sin(1πx - 2) - 3) + 4) + 1 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1cos(1π(-2|(-5(-3x^2 + 3x) - 1) - 1| - 2) - 2) + 2 negative?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|((-3(-2sin(2πx + 2) + 2))/(-3(-2sin(2πx + 2) + 2) - 2))| + 1 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 5(4((3(-3sin(2πx + 2)) - 1)/(2(-3sin(2πx + 2)) + 2)) + 2)^2 + 3(4((3(-3sin(2πx + 2)) - 1)/(2(-3sin(2πx + 2)) + 2)) + 2) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(-5(3(2cos(1πx - 1) - 1)^2 + 2(2cos(1πx - 1) - 1) + 3) - 4) + 1| - 2 is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3cos(3π(-2|(-3x + 1) - 3| - 1) - 1) - 3 positive?

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[User]
For the function f(x) = 3(-2|(-3cos(1πx - 3))| - 3) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(-2(-1sin(3πx - 1) - 1) + 5)^2 - 1(-2(-1sin(3πx - 1) - 1) + 5) + 3 is strictly decreasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(3|(1cos(2πx + 3) - 3) + 1| - 3)^2 - 3(3|(1cos(2πx + 3) - 3) + 1| - 3) - 5 negative?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-3(-5(-2sin(2πx - 2) - 1)^2 - 4(-2sin(2πx - 2) - 1) + 4) - 3)/(3(-5(-2sin(2πx - 2) - 1)^2 - 4(-2sin(2πx - 2) - 1) + 4) - 2) is strictly decreasing.

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[User]
For the function f(x) = 1(-1(-2cos(3πx - 3) + 2) - 1)^2 - 2(-1(-2cos(3πx - 3) + 2) - 1) - 4, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = (-1(-1sin(1π(-4(2|x + 3| - 3) + 5) + 3) + 2) - 1)/(3(-1sin(1π(-4(2|x + 3| - 3) + 5) + 3) + 2) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
For the function f(x) = -5((-1(-4(-3cos(1πx + 3) - 3)^2 - 5(-3cos(1πx + 3) - 3)) + 1)/(3(-4(-3cos(1πx + 3) - 3)^2 - 5(-3cos(1πx + 3) - 3)) + 2)) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(1sin(2π(-3|x - 2| + 2) - 3))^2 + 1(1sin(2π(-3|x - 2| + 2) - 3)) + 4 positive?

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[User]
For the function f(x) = 1(-3(-1sin(1πx + 3) + 3)^2 - 2(-1sin(1πx + 3) + 3) + 3) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 5(5(1cos(2πx + 3) + 1)^2 + 2(1cos(2πx + 3) + 1)) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 4((-2(-2cos(1π(-1|x + 2| - 2) - 3) + 3) + 1)/(-3(-2cos(1π(-1|x + 2| - 2) - 3) + 3) + 2)) + 5 positive?

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[User]
For the function f(x) = 3cos(3π(-2|(-3((-3x - 1)/(-3x + 4)) + 2) - 2| - 1) - 3), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2(2cos(3π(1x^2 - 5x) + 2) - 1) + 4 positive?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(-1cos(3π(1x + 5) - 3) - 2) + 1)/(1(-1cos(3π(1x + 5) - 3) - 2)) is strictly decreasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3|(4(1sin(1πx + 2) + 2)^2 + 4(1sin(1πx + 2) + 2) - 3) + 3| - 2 is strictly increasing.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -4(-1sin(1π(-1(3|x + 1| + 3)^2 - 5(3|x + 1| + 3) + 4) + 1) + 1) - 3 negative?

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(-4(-2(3cos(3πx - 1) - 2) - 1)^2 + 2(-2(3cos(3πx - 1) - 2) - 1) - 4) + 2)/(-1(-4(-2(3cos(3πx - 1) - 2) - 1)^2 + 2(-2(3cos(3πx - 1) - 2) - 1) - 4) + 3) positive?

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(2(2sin(2πx - 2) + 2)^2 + 3) - 1 is strictly increasing.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3sin(3π(-2|(-3(1x^2 + 4x - 2) - 2) - 2| - 1) + 2) - 3 is strictly increasing.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = 1|(1cos(1π(-5x^2 - 4) - 1) - 1) - 3| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

Present the answer in LaTex format: \boxed{Your answer}


[User]
For the function f(x) = -2|((3(-2sin(1π(-3x + 3) - 3) - 3) - 2)/(-3(-2sin(1π(-3x + 3) - 3) - 3) + 4)) - 3| + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2cos(1π(-5(-2|x + 3| + 2) - 2) + 3) - 1 negative?

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(2|(-1sin(1πx) + 1) - 1| - 1) negative?

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[User]
For the function f(x) = 3sin(3π(2(-1|((2x + 3)/(-2x + 3)) + 2|) + 3) - 1) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(3sin(1π(-2|(-1x^2 + 4x - 3) - 1| - 1) - 3) + 3) - 2)/(-1(3sin(1π(-2|(-1x^2 + 4x - 3) - 1| - 1) - 3) + 3) + 3) is strictly decreasing.

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[User]
For the function f(x) = 4((-1(1(-1sin(1πx + 1)) - 2) + 3)/(-1(1(-1sin(1πx + 1)) - 2) - 3))^2 - 1((-1(1(-1sin(1πx + 1)) - 2) + 3)/(-1(1(-1sin(1πx + 1)) - 2) - 3)) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(1π(-3|((-3x + 1)/(-1x)) - 2| + 3) + 1) + 3 positive?

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[User]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2cos(1π((3(2|(1x^2 - 2x) - 1| - 1) - 2)/(1(2|(1x^2 - 2x) - 1| - 1))) + 3) - 2 positive?

Present the answer in LaTex format: \boxed{Your answer}