messages listlengths 1 1 | ground_truth stringclasses 87
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(5(3cos(2πx - 1) + 2) - 1) + 2| + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "For the function f(x) = 2cos(2π(3(-3x - 1) - 3) + 2) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(2sin(2π(-2|x + 2| + 1))) + 3| + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 5(-2sin(1π(4x + 3) - 1) + 2)^2 - 5(-2sin(1π(4x + 3) - 1) + 2) + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(2sin(3π((-1x)/(2x - 3)) - 1) + 1)^2 - 3(2sin(3π((-1x)/(2x - 3)) - 1) + 1) + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "For the function f(x) = 1cos(1π((-2(2x^2 - 2x + 4) + 3)/(-1(2x^2 - 2x + 4) + 3)) - 1) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3(-2(-2sin(3πx) - 1) - 5) + 2)/(-3(-2(-2sin(3πx) - 1) - 5) - 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "For the function f(x) = 5((-3(-2cos(1πx + 3) + 3) - 3)/(3(-2cos(1πx + 3) + 3) - 2)) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3sin(3π(4((3x - 2)/(-3x)) + 2) + 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "For the function f(x) = 1((1(-2sin(2πx - 1) - 3) - 2)/(1(-2sin(2πx - 1) - 3) + 2))^2 + 1((1(-2sin(2πx - 1) - 3) - 2)/(1(-2sin(2πx - 1) - 3) + 2)) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 41 | MATH |
[
{
"content": "For the function f(x) = -1(2|(1sin(3πx - 2) + 2)| - 1) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3(1(1cos(3πx + 2) + 2) + 5) - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|(-3sin(1π(-5x + 5) - 1) + 3) + 2| - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(-2(-1sin(3πx + 1) + 1) - 5) - 1)/(-2(-2(-1sin(3πx + 1) + 1) - 5)) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1((-2(1sin(3πx - 3) - 1) + 2)/(2(1sin(3πx - 3) - 1) + 2))^2 + 1((-2(1sin(3πx - 3) - 1) + 2)/(2(1sin(3πx - 3) - 1) + 2)) + 5 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 60 | MATH |
[
{
"content": "For the function f(x) = (3(4(-2sin(1πx - 2) + 2) - 5) + 3)/(1(4(-2sin(1πx - 2) + 2) - 5)), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2cos(1π(1(4x + 2)^2 - 3(4x + 2) + 5) - 3) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(-2sin(2π(2x^2 - 5) - 2) - 3) - 1)/(-2(-2sin(2π(2x^2 - 5) - 2) - 3) - 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "For the function f(x) = -1|(-3|(-1cos(3πx + 2) + 3) - 1| - 1) - 1|, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3sin(2π((2((1x + 2)/(3x - 2)) - 2)/(1((1x + 2)/(3x - 2)) + 2)) + 2) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(3sin(1π(3x + 3) - 3)) - 2)/(1(3sin(1π(3x + 3) - 3)) + 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1cos(2π(-1(2x^2 - 2x - 4) + 4) - 1) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2sin(1π(1|((3x - 1)/(3x + 1)) - 2| + 2) - 2) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|(-1|(-3cos(1πx - 1) - 2) + 3| + 1) - 2| is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|(-2(2cos(2πx) + 1) + 3) - 2| + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(-1cos(2π(3x^2 - 4x + 3) - 3) + 3)^2 - 1(-1cos(2π(3x^2 - 4x + 3) - 3) + 3) + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|(-3sin(2π(1x + 4) - 1) + 1) + 1| - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "For the function f(x) = 3cos(2π(3((2x - 2)/(3x + 2))^2 + 3((2x - 2)/(3x + 2))) - 1) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2sin(3π(1|((3x - 1)/(3x)) - 1|) + 1) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "For the function f(x) = -3cos(3π(-1|(3x^2 - 3x)| + 1)) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(-2cos(2π(-5x^2 + 3x) + 1)) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1sin(2π(2|(-1|x + 3| + 2) + 1| + 2) - 2) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(-3sin(1π(1x - 2) + 1) + 3)^2 + 4(-3sin(1π(1x - 2) + 1) + 3) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(3sin(3π(5x^2 + 4x) - 3) - 3) + 2)/(-2(3sin(3π(5x^2 + 4x) - 3) - 3) + 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(-1|(1cos(2πx + 1) + 2) - 1| - 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(-4(3sin(3πx - 2) - 1)^2 + 5(3sin(3πx - 2) - 1) + 3) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3(3sin(2π((-3x - 3)/(1x + 2)) + 2)) + 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2cos(1π(3(3x + 3)^2 + 4(3x + 3) + 4) - 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "For the function f(x) = (-2(-3cos(3π((-2x - 1)/(3x - 1))) + 1) + 2)/(-3(-3cos(3π((-2x - 1)/(3x - 1))) + 1) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "For the function f(x) = 1(-3cos(3π(4x^2 + 5x - 1) + 3) + 1)^2 - 4(-3cos(3π(4x^2 + 5x - 1) + 3) + 1) - 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "For the function f(x) = 3(-3(3cos(3πx - 2) + 3) + 2) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(1π(-2|(-2|x - 2| - 1) - 3| + 2) - 3) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1cos(1π(2((2x + 3)/(-3x - 1))^2 + 2((2x + 3)/(-3x - 1)) - 5) + 2) + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|(-3sin(2π((3x + 2)/(1x)) + 2) - 3)| + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1sin(2π(-3|(3x - 5) + 2| + 1)) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(1cos(3π(-3|x - 2|) + 1) + 3) + 2)/(-2(1cos(3π(-3|x - 2|) + 1) + 3)) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 91 | MATH |
[
{
"content": "For the function f(x) = -2((1(-1cos(1πx + 2) - 2) + 1)/(2(-1cos(1πx + 2) - 2) + 3))^2 - 3((1(-1cos(1πx + 2) - 2) + 1)/(2(-1cos(1πx + 2) - 2) + 3)) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 21 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2sin(2π((2(2x^2 + 4x + 2) - 1)/(3(2x^2 + 4x + 2)))) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1sin(3π(1(3|x - 2| - 3) - 1) + 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 91 | MATH |
[
{
"content": "For the function f(x) = -3sin(3π((-1(-5x + 5) - 3)/(-2(-5x + 5) + 3)) + 1) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "For the function f(x) = 1sin(3π((1((-2x - 2)/(2x - 1)) + 2)/(2((-2x - 2)/(2x - 1)) + 2)) + 3) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(-4(2cos(1πx - 1))^2 + 2(2cos(1πx - 1)) - 2)| + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(1sin(1π(-5x^2 + 4x + 3) - 2) + 1) + 1)/(-1(1sin(1π(-5x^2 + 4x + 3) - 2) + 1) - 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 53 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(-2sin(3π(-3|x|) + 1) + 1) - 3| + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 91 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(3cos(3π(3x^2 - 4x + 1) + 3) - 3) + 1)/(2(3cos(3π(3x^2 - 4x + 1) + 3) - 3) - 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "For the function f(x) = 3cos(3π(1|(1x - 4) + 3| + 2) + 3) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 5(1(2cos(1πx - 2) + 2) + 4) - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(-2|(3sin(2πx + 3)) + 1| + 3) - 2)/(-2(-2|(3sin(2πx + 3)) + 1| + 3) - 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3|(-3(2sin(2πx - 2) - 3)^2 + 5(2sin(2πx - 2) - 3) + 1)| + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(-2(1cos(2πx) - 1)^2 - 3(1cos(2πx) - 1) + 1)^2 - 5(-2(1cos(2πx) - 1)^2 - 3(1cos(2πx) - 1) + 1) + 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 60 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(1cos(3π(2|x - 1|) - 1)) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3cos(2π(-1(1|x + 3| - 1)^2 - 3(1|x + 3| - 1) + 2) - 2) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3(-3(3sin(2πx - 3))^2 + 5(3sin(2πx - 3)) + 5) - 3)/(2(-3(3sin(2πx - 3))^2 + 5(3sin(2πx - 3)) + 5)) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(2(-3cos(3πx + 2) - 1)^2 - 4(-3cos(3πx + 2) - 1) + 5)^2 - 2(2(-3cos(3πx + 2) - 1)^2 - 4(-3cos(3πx + 2) - 1) + 5) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 24 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(-2cos(1π(-2x + 5) - 2) + 2)^2 - 1(-2cos(1π(-2x + 5) - 2) + 2) - 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(2sin(2π(3|x| - 2) + 1) - 2) - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(-1sin(1π(-3|x - 2| - 1)) - 1) + 1)/(3(-1sin(1π(-3|x - 2| - 1)) - 1) + 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2cos(1π(1(-2x^2 + 1x - 2)^2 - 2(-2x^2 + 1x - 2) - 4)) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1cos(3π((-1(2x + 2) + 3)/(-1(2x + 2) - 2)) - 2) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "For the function f(x) = -5(2(3sin(1πx + 1)) - 1)^2 + 1(2(3sin(1πx + 1)) - 1) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "For the function f(x) = -2cos(1π(-3(-3x^2 - 1x - 4) + 2) + 1) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|(-3|(-2cos(1πx + 1) + 2) - 2| - 1) + 2| - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(-3cos(2π(-4x - 3) - 1) - 1) + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2sin(3π(-3|(1x^2 - 5x - 2) + 3| + 3) + 1) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(-2sin(2π(1|x + 2| + 2) - 2) + 3)^2 - 5(-2sin(2π(1|x + 2| + 2) - 2) + 3) - 4 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "For the function f(x) = (2(-4(-2sin(2πx + 1) + 1) - 4) + 3)/(1(-4(-2sin(2πx + 1) + 1) - 4) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "For the function f(x) = -5(3|(1cos(3πx - 1) + 3) - 1| + 1)^2 - 5(3|(1cos(3πx - 1) + 3) - 1| + 1) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "For the function f(x) = 3|(-3(2|x + 3| - 3)^2 + 3(2|x + 3| - 3) + 5) - 3| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "For the function f(x) = (-3((3(3sin(3πx + 1) - 3) + 2)/(-1(3sin(3πx + 1) - 3))))/(-1((3(3sin(3πx + 1) - 3) + 2)/(-1(3sin(3πx + 1) - 3))) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 30 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1((-2(-1cos(3πx - 3) + 3) + 2)/(2(-1cos(3πx - 3) + 3) - 1))^2 + 3((-2(-1cos(3πx - 3) + 3) + 2)/(2(-1cos(3πx - 3) + 3) - 1)) + 5 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 30 | MATH |
[
{
"content": "For the function f(x) = 1(3cos(2π(-2x^2 - 3x + 5) + 3))^2 - 4, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(2sin(2π(1x + 4) + 3) + 2) + 2| positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "For the function f(x) = 1sin(3π(4(2|x + 1| + 3) - 5) - 3) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2cos(3π(3|(2x) + 1| - 3) - 3) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3(3|(-1cos(3πx + 2) - 1) - 2| - 3)^2 - 2(3|(-1cos(3πx + 2) - 1) - 2| - 3) + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2(1cos(3π(-5x - 5) + 1) + 2) - 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(-3cos(2π((-1x)/(3x - 2)) - 1) - 2))/(-2(-3cos(2π((-1x)/(3x - 2)) - 1) - 2) - 1) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2cos(2π(-2(2|x| + 2) + 1) + 2) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81 | MATH |
[
{
"content": "For the function f(x) = -2sin(2π(2(1|x + 2| + 2)^2 + 1(1|x + 2| + 2) - 4) - 1) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 5(-3cos(1π(3|x + 1| - 2)) + 3) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(1cos(2π((2x)/(1x + 1)) - 3) + 3) - 1| - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "For the function f(x) = -1(-3(-3cos(2πx - 1) - 2) + 5) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "For the function f(x) = 1(2sin(2π(-5x - 3)) + 2) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 109 | MATH |
[
{
"content": "For the function f(x) = 3(3cos(3π(5x^2 - 2x + 1) + 3) + 3)^2 - 2(3cos(3π(5x^2 - 2x + 1) + 3) + 3) - 4, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|(2cos(2π((-3x - 2)/(-2x + 3)))) - 3| positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "For the function f(x) = 4(5(-2cos(3πx - 2) + 1))^2 + 5(5(-2cos(3πx - 2) + 1)) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "For the function f(x) = 1sin(1π(1|(-4x + 1) + 2| - 2) - 3) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "For the function f(x) = 3(-3sin(3π((3x - 3)/(-1x)) - 2) - 3)^2 - 2(-3sin(3π((3x - 3)/(-1x)) - 2) - 3) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-3(1sin(1π(3|x - 1| - 3) - 2) + 2) + 3)/(-2(1sin(1π(3|x - 1| - 3) - 2) + 2) - 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "For the function f(x) = -3|(-1cos(2π((-2x + 3)/(3x)) + 1) - 2) + 1| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.