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

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


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

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


[User]
For the function f(x) = -3|(-1(3sin(1π((1x - 1)/(-1x + 3))) + 3) + 5) - 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) = -4(-2cos(2πx - 2) + 2)^2 - 5(-2cos(2πx - 2) + 2) + 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) = -3(-2sin(2π(-3((2x + 3)/(-3x - 2))^2 - 5((2x + 3)/(-3x - 2)) - 2) - 1) - 1) + 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(-1sin(2πx - 1) - 3)^2 + 3(-1sin(2πx - 1) - 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) = -1|(-5(2cos(3πx - 3) + 3)^2 + 5(2cos(3πx - 3) + 3) - 3) - 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) = -2e^(1(-1|((-1x)/(-3x + 1)) - 3| - 3)) - 3 is strictly increasing.

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


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

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


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

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


[User]
For the function f(x) = -1sin(3π(-1|x - 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|(5((-2x - 2)/(1x - 2))^2 - 1((-2x - 2)/(1x - 2)) - 5) - 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) = 3sin(3π(2((1(-2|x| - 1) + 3)/(3(-2|x| - 1) - 2)) + 4) - 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) = (3(-2sin(1πx - 1) + 1))/(-2(-2sin(1πx - 1) + 1) + 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) = 1(-1sin(1π((3(3x + 5) + 1)/(-1(3x + 5) + 2)) + 2) + 2)^2 - 3(-1sin(1π((3(3x + 5) + 1)/(-1(3x + 5) + 2)) + 2) + 2) + 5 is strictly increasing.

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


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

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


[User]
For the function f(x) = 1cos(3π(-4x - 5) + 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) = -1(-1sin(2πx + 2) - 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) = 1(-3(-3cos(2πx + 3) + 3)^2 - 4(-3cos(2πx + 3) + 3) + 1) + 5 negative?

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


[User]
For the function f(x) = 1cos(3π(-5(-1|(-4x^2 + 3x + 4) + 3| - 2) + 5) + 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(3|(1(-2cos(2πx - 1) + 3) - 2) - 2| + 1)^2 - 3(3|(1(-2cos(2πx - 1) + 3) - 2) - 2| + 1) - 2 is strictly decreasing.

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


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

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


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

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


[User]
For the function f(x) = 4(-3sin(1π(-1|x - 2| - 3) - 2) + 3)^2 + 5(-3sin(1π(-1|x - 2| - 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) = 2sin(2π(-4x^2 - 4) + 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(2|(-2cos(1πx + 2) - 1) + 3| + 3) + 5 is strictly increasing.

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


[User]
For the function f(x) = 2(2((2(-3|x - 3|) + 3)/(1(-3|x - 3|) - 2))^2 - 5((2(-3|x - 3|) + 3)/(1(-3|x - 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) = (3(2cos(1πx + 1) - 1) + 2)/(2(2cos(1πx + 1) - 1) + 2) is strictly increasing.

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


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

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


[User]
For the function f(x) = 1|(1cos(1πx - 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) = 1|(-5(5((-2x - 2)/(1x + 2)))^2 + 4(5((-2x - 2)/(1x + 2))) + 3) - 1| + 1 positive?

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


[User]
For the function f(x) = -2|(-2((2x + 2)/(2x - 1))^2 + 2((2x + 2)/(2x - 1)) - 2) + 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) = (3(-2|(2(-1cos(3πx + 1) + 3)^2 + 1(-1cos(3πx + 1) + 3))| + 1) + 1)/(3(-2|(2(-1cos(3πx + 1) + 3)^2 + 1(-1cos(3πx + 1) + 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]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3e^(1(3((-1x)/(2x - 1))^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) = 4(4((1(2|x - 3| + 1) + 3)/(3(2|x - 3| + 1) - 2)) - 3)^2 - 4(4((1(2|x - 3| + 1) + 3)/(3(2|x - 3| + 1) - 2)) - 3) negative?

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


[User]
For the function f(x) = 4(-1|(2sin(2πx - 1) + 2) - 3| + 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) = -5(1cos(1πx + 2) + 2)^2 - 5(1cos(1πx + 2) + 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) = -2cos(1π(2(-1|((-3x - 3)/(3x - 1)) + 1| + 2)^2 - 3(-1|((-3x - 3)/(3x - 1)) + 1| + 2) - 5) + 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) = 4(-1(3|((3x)/(-1x - 2)) + 2| - 2)^2 + 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]
For the function f(x) = (-1(-1cos(1π(-2(3|x - 3| - 2)^2 + 5(3|x - 3| - 2) + 2) + 3)) - 1)/(1(-1cos(1π(-2(3|x - 3| - 2)^2 + 5(3|x - 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]
On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3((2(-2|x - 3| + 2) - 1)/(-3(-2|x - 3| + 2) - 2))^2 + 4((2(-2|x - 3| + 2) - 1)/(-3(-2|x - 3| + 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) = 2(-1(-3|x - 2| + 1)^2 + 1(-3|x - 2| + 1) - 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) = 2((2(2cos(3π(-4x + 3) + 2) - 2) + 1)/(-1(2cos(3π(-4x + 3) + 2) - 2) + 3))^2 + 2((2(2cos(3π(-4x + 3) + 2) - 2) + 1)/(-1(2cos(3π(-4x + 3) + 2) - 2) + 3)) + 4 is strictly increasing.

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


[User]
For the function f(x) = 2sin(2π(-5(-1|(-1x^2 - 1x - 3) - 1| - 2) - 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) = 2(2|(2cos(2πx - 2) - 2) - 1| - 2)^2 - 5 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|(-3e^(-1(-2((-1x - 2)/(3x))^2 - 1((-1x - 2)/(3x)) - 5)) - 2) - 1| + 2 negative?

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


[User]
For the function f(x) = 3cos(3π(-3|((1x + 3)/(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) = 2sin(2π(-2|x - 2| + 2)) + 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) = -1(4((-2(-2|x + 2| + 3) + 2)/(-2(-2|x + 2| + 3) + 1))^2 - 4) - 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(2cos(2πx + 3) + 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) = -3cos(1π(1(5x^2 + 2x - 5) - 4) - 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) = (2(2cos(3πx + 3) - 3))/(2(2cos(3πx + 3) - 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) = -2|(1sin(2π((1x)/(3x - 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) = 2|((-2x)/(1x + 2)) - 1| - 1 positive?

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


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

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


[User]
For the function f(x) = 2|((-2(1x + 1) + 3)/(-3(1x + 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|(5((1x + 1)/(3x - 2)) - 1)| + 1 is strictly decreasing.

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


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

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


[User]
For the function f(x) = 1sin(2π(4x - 4) - 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) = 2cos(3π((2x - 2)/(-1x - 2)) + 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) = -4((1(-3(-3|x - 3| + 2) + 3) - 1)/(-2(-3(-3|x - 3| + 2) + 3) + 1))^2 - 4((1(-3(-3|x - 3| + 2) + 3) - 1)/(-2(-3(-3|x - 3| + 2) + 3) + 1)) + 4 positive?

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


[User]
For the function f(x) = 3|(-1e^(-2(-2(-3x^2 + 1x) - 2)) - 1) + 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) = -1|(-2((2(1x) + 1)/(1(1x) - 2))^2 - 1((2(1x) + 1)/(1(1x) - 2)) + 2) + 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) = 4(3(-2sin(2π(-1|x| - 2) - 3) + 1)^2 - 2(-2sin(2π(-1|x| - 2) - 3) + 1) + 3) - 5 negative?

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[User]
For the function f(x) = -5(1|(1x^2 + 2x) - 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) = -2|((-1(5(-1x - 1)^2 + 2(-1x - 1) - 4) - 2)/(-3(5(-1x - 1)^2 + 2(-1x - 1) - 4) + 2)) + 1| positive?

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

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[User]
For the function f(x) = (2(-1|(-2sin(2πx - 1) + 3)| - 2))/(-1(-1|(-2sin(2πx - 1) + 3)| - 2) + 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|(3(-1x^2 - 5x + 3) - 4) + 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) = -5((1(5(1cos(2πx - 2) + 2)) + 1)/(-3(5(1cos(2πx - 2) + 2)) - 1))^2 + 1((1(5(1cos(2πx - 2) + 2)) + 1)/(-3(5(1cos(2πx - 2) + 2)) - 1)) - 2 negative?

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

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

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

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[User]
For the function f(x) = (1(-2sin(3π(3(-3x + 5)^2 - 3(-3x + 5)) + 3) - 3) + 2)/(-2(-2sin(3π(3(-3x + 5)^2 - 3(-3x + 5)) + 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) = 1(1sin(1π(-3((1x - 1)/(-2x + 1)) - 1) - 2) - 2)^2 + 2(1sin(1π(-3((1x - 1)/(-2x + 1)) - 1) - 2) - 2) + 3 positive?

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[User]
For the function f(x) = 2|(-1sin(3π((3(1x^2 - 5x + 2))/(3(1x^2 - 5x + 2) + 2)) - 1) + 1) - 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(4((-2(-2sin(1πx + 1)) - 2)/(-1(-2sin(1πx + 1)))) + 3)^2 + 3(4((-2(-2sin(1πx + 1)) - 2)/(-1(-2sin(1πx + 1)))) + 3) - 5 is strictly increasing.

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

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

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


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

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

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[User]
For the function f(x) = -1(-3(2sin(3πx + 2) - 1) - 4)^2 - 2(-3(2sin(3πx + 2) - 1) - 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]
Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(5((3x - 3)/(-3x + 2)) + 3) - 1| + 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|(-3sin(3π((-3x - 1)/(2x + 2)) - 1) - 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) = -1(4(-1|x - 1|) + 5)^2 - 5(4(-1|x - 1|) + 5) - 2 positive?

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


[User]
For the function f(x) = 4(-2|(-2cos(3π((1x - 2)/(-1x + 3)) + 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) = 3(1|(3((-2x - 3)/(3x - 2)) + 5) + 1| - 3)^2 - 1(1|(3((-2x - 3)/(3x - 2)) + 5) + 1| - 3) + 1 positive?

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

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

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[User]
For the function f(x) = -1sin(2π((2x - 3)/(-2x - 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) = -3(1cos(2π((-1x - 2)/(-1x - 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(2π(-2|x + 2| + 2) + 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) = -3sin(1π(-4(2|x - 2| + 3)^2 - 5(2|x - 2| + 3) - 5) + 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) = -4(3|((-2(2sin(2πx + 3) + 3) - 1)/(1(2sin(2πx + 3) + 3))) - 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) = -1((3(1|x| - 2) - 3)/(2(1|x| - 2) + 1))^2 - 3((3(1|x| - 2) - 3)/(2(1|x| - 2) + 1)) - 5 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(3cos(3π((-2x - 1)/(-3x - 2)) + 1) - 2)^2 - 1(3cos(3π((-2x - 1)/(-3x - 2)) + 1) - 2) + 3 is strictly decreasing.

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


[User]
For the function f(x) = 3sin(1π(-5((-3(4x - 1) - 2)/(-3(4x - 1)))^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|(-2(4(3cos(3πx - 2) - 1) - 4)^2 + 4(4(3cos(3πx - 2) - 1) - 4) + 4) + 1| - 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) = -3((-1x + 3)/(-1x + 2))^2 + 5((-1x + 3)/(-1x + 2)) + 5 is strictly decreasing.

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


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

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


[User]
For the function f(x) = 1(-1e^(-1((-2x - 3)/(-2x - 1))) - 1)^2 + 3(-1e^(-1((-2x - 3)/(-2x - 1))) - 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) = 2|(-1((-2x + 2)/(1x + 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]
For the function f(x) = -3sin(2π((3(1(2|x - 1| - 3)^2 - 1(2|x - 1| - 3) + 4))/(3(1(2|x - 1| - 3)^2 - 1(2|x - 1| - 3) + 4) + 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) = -3sin(2π(-4(-3x - 4)^2 + 1(-3x - 4) - 4) + 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) = 1|(4(4((1x)/(-2x + 1)) + 1)^2 + 2) + 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) = 4(2cos(1πx + 3) - 2)^2 - 2(2cos(1πx + 3) - 2) + 4 is strictly increasing.

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