id
string | setting_key
string | difficulty
string | level
int32 | messages
dict | ground_truth
string | dataset
string | omega_split
string |
|---|---|---|---|---|---|---|---|
math_algebra_func_derivative_sign_level_2_2_0
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|((-3(-2sin(1πx - 2) + 2) + 2)/(2(-2sin(1πx - 2) + 2) + 1)) - 1| positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
20
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_1
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1sin(1π(3(3x^2 - 2x + 5)^2 + 1(3x^2 - 2x + 5) - 2) + 3) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
12
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_2
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(2π(-1|(3|x + 3|)| + 2) - 2) - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
60
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_3
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 4(-1(-5x^2 + 1)^2 - 4(-5x^2 + 1) - 2)^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}"
]
}
|
4
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_4
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -3(-3(-3sin(1πx + 3) - 3) + 5)^2 + 5(-3(-3sin(1πx + 3) - 3) + 5) + 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}"
]
}
|
11
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_5
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(-4(-2sin(1πx - 2) + 1) - 4)| + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_6
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2(3|(1sin(1πx - 1) + 1) - 1|) + 1)/(3(3|(1sin(1πx - 1) + 1) - 1|) + 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
21
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_7
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3sin(3π(-5(-2x - 4)) - 2) - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
100
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_8
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1cos(1π(-1(4x^2 + 3x - 5)^2 - 5(4x^2 + 3x - 5) + 4) + 1) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_9
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(5(1cos(3πx + 1) - 3)^2 + 3(1cos(3πx + 1) - 3) - 1) - 3)/(-2(5(1cos(3πx + 1) - 3)^2 + 3(1cos(3πx + 1) - 3) - 1) - 1) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
30
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_10
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(2cos(2π((2x - 1)/(-2x + 3)) + 1)) - 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_11
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(2π(-2(-2|x - 3|) - 2) - 1) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
80
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_12
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -1cos(2π(-1|((-3x - 3)/(1x)) - 2| + 3) + 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}"
]
}
|
11
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_13
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2cos(3π((1(-3|x - 1| + 3) + 2)/(2(-3|x - 1| + 3) + 2)) - 2) - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_14
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(2cos(2π(1x^2 + 4x + 4))) + 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
47
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_15
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(-1cos(2π(-1x^2 - 2x - 1) + 1) - 3)^2 - 3(-1cos(2π(-1x^2 - 2x - 1) + 1) - 3) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
36
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_16
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(2|(-3cos(2πx - 1) + 2) - 3|) - 2)/(3(2|(-3cos(2πx - 1) + 2) - 3|)) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
41
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_17
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -1(-1cos(1π((-3x + 2)/(-1x + 3)) - 1))^2 + 2(-1cos(1π((-3x + 2)/(-1x + 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}"
]
}
|
10
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_18
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2sin(1π(-2((3x - 3)/(1x - 2))^2 - 3((3x - 3)/(1x - 2)) + 2) + 1) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
27
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_19
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(1sin(1π(-4x^2 - 1x + 5) + 3) + 1)^2 + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
37
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_20
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3sin(1π(3((-1x + 2)/(1x + 3))^2 + 4((-1x + 2)/(1x + 3)) - 1) - 1) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
21
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_21
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|(-1(-3x^2 - 3x + 4)^2 - 4(-3x^2 - 3x + 4) - 2) - 1| + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_22
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(1cos(1π(-3x^2 - 2x - 3) - 2) - 3) + 2)/(1(1cos(1π(-3x^2 - 2x - 3) - 2) - 3)) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
49
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_23
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 3|(-2(2cos(2πx - 3) + 2) - 1) - 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}"
]
}
|
21
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_24
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -4(2|(-1sin(1πx + 1)) - 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}"
]
}
|
11
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_25
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3cos(2π(-1(2x^2 - 1x + 3) + 1)) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
50
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_26
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 3cos(3π(1(3|x + 3| - 1)) - 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}"
]
}
|
90
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_27
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(-2|(3sin(1πx + 3) + 3) - 1|)^2 - 3(-2|(3sin(1πx + 3) + 3) - 1|) + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
21
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_28
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1cos(2π(-5(-3|x + 3| - 1)^2 - 1(-3|x + 3| - 1)) - 2) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
16
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_29
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 1sin(2π(4((1x + 3)/(-1x))^2 - 3((1x + 3)/(-1x)) - 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}"
]
}
|
22
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_30
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(-5(1sin(2πx + 2) - 1) + 5)^2 - 1(-5(1sin(2πx + 2) - 1) + 5) - 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
21
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_31
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(-3(1sin(3πx - 1) + 3)^2 - 1(1sin(3πx - 1) + 3) + 2)^2 - 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_32
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(1(3sin(3πx - 1) - 3) - 5) + 1)/(-3(1(3sin(3πx - 1) - 3) - 5)) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
30
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_33
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(1sin(1π(-4x^2 + 3x - 2) + 3) + 3) + 1| + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
54
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_34
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(1π(-4((1x - 1)/(3x - 2)) + 5) - 2) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_35
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -5(1cos(2π(4x^2 - 5x + 5)) + 2)^2 - 5(1cos(2π(4x^2 - 5x + 5)) + 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}"
]
}
|
16
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_36
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = (-1(-3(-3cos(1πx - 1) + 1)^2 - 4(-3cos(1πx - 1) + 1) - 3) + 1)/(2(-3(-3cos(1πx - 1) + 1)^2 - 4(-3cos(1πx - 1) + 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}"
]
}
|
20
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_37
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(1(2cos(3πx - 3) - 1)^2 + 5) + 1| - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
60
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_38
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1sin(1π(-1|(-3|x - 2| + 2) - 3| - 2) + 1) + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
31
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_39
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-3(1|(3cos(3πx - 3) - 1) + 1| - 1) + 1)/(1(1|(3cos(3πx - 3) - 1) + 1| - 1) - 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
60
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_40
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 5(-2(-2cos(1πx) + 1)^2 + 3(-2cos(1πx) + 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}"
]
}
|
20
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_41
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2((-1(3cos(2πx + 1) - 3) + 1)/(-3(3cos(2πx + 1) - 3) - 1)) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
20
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_42
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3(-4(1cos(1πx - 3))^2 - 4)^2 + 5(-4(1cos(1πx - 3))^2 - 4) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
20
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_43
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(3cos(2π(1x^2 + 2x - 1) + 1) + 1) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
56
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_44
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3cos(2π(-1(-1x + 5) - 3) + 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
21
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_45
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(-1cos(3π(2|x| - 1) - 3) - 1)^2 - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
60
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_46
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1sin(2π(-2|(-5x^2 - 3x - 4) - 3| + 2)) + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
51
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_47
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -1sin(3π(3(-5x)^2 + 4(-5x)) - 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}"
]
}
|
14
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_48
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(-2sin(2π(-4x + 3) - 2) - 2) + 2)/(-2(-2sin(2π(-4x + 3) - 2) - 2) - 1) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
63
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_49
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2sin(2π((1(-1|x| + 3))/(-2(-1|x| + 3) + 3)) + 1) + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_50
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(1(1cos(2πx - 3) - 3) + 3) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
21
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_51
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|((2(3cos(3πx + 2) - 3) - 2)/(1(3cos(3πx + 2) - 3) - 2)) + 1| + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
30
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_52
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 1|(-2(-2cos(2πx + 3) - 1)^2 + 2(-2cos(2πx + 3) - 1)) - 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}"
]
}
|
40
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_53
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2sin(2π(-3((-1x + 2)/(-2x + 3))^2 - 5((-1x + 2)/(-2x + 3)) + 3) + 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_54
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 3(5(2cos(1πx + 3) - 3)^2 + 4(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}"
]
}
|
11
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_55
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 4(-5(-2sin(3πx + 3) - 1)^2 - 5(-2sin(3πx + 3) - 1) - 1)^2 + 4(-5(-2sin(3πx + 3) - 1)^2 - 5(-2sin(3πx + 3) - 1) - 1) - 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}"
]
}
|
16
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_56
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -1(-3|(-1x^2 + 4x + 4) + 1| + 2)^2 - 5(-3|(-1x^2 + 4x + 4) + 1| + 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}"
]
}
|
4
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_57
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(1(-1sin(2πx) + 3)^2 + 1(-1sin(2πx) + 3) - 4) - 2| + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
20
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_58
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2((-3(1sin(1πx - 2) - 2) - 3)/(1(1sin(1πx - 2) - 2) - 3)) + 4 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_59
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|(3cos(1π(3x - 2) - 2) + 1) + 2| + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
31
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_60
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(2π(-4(-2|x + 1| + 2) + 2) - 3) + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
41
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_61
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -2sin(3π((1((2x + 3)/(-1x + 2)) + 2)/(-2((2x + 3)/(-1x + 2)))) - 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}"
]
}
|
9
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_62
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -1(2|(-3cos(3πx + 3) - 2) + 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}"
]
}
|
61
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_63
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 2(1sin(2π(1x^2 + 4x - 2) + 3) + 3) + 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}"
]
}
|
49
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_64
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(2sin(1π(5x^2 - 2x - 4) - 3) - 2))/(-1(2sin(1π(5x^2 - 2x - 4) - 3) - 2) - 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
37
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_65
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -4((-1(1cos(1πx + 2) - 2) + 2)/(3(1cos(1πx + 2) - 2) + 3))^2 + 5((-1(1cos(1πx + 2) - 2) + 2)/(3(1cos(1πx + 2) - 2) + 3)) + 5 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_66
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 4(3(-3cos(1πx - 3) - 1) - 4) + 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}"
]
}
|
11
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_67
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 2|((-2(3cos(1πx + 2) + 1) + 1)/(1(3cos(1πx + 2) + 1) - 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}"
]
}
|
31
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_68
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = (2((-1(3cos(2πx) - 1) - 1)/(-1(3cos(2πx) - 1) + 2)) - 2)/(1((-1(3cos(2πx) - 1) - 1)/(-1(3cos(2πx) - 1) + 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}"
]
}
|
20
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_69
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 1sin(3π(3(-2x + 3) + 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}"
]
}
|
21
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_70
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(-2cos(3π((-2x + 2)/(2x)) + 1) - 2))/(-3(-2cos(3π((-2x + 2)/(2x)) + 1) - 2) + 2) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_71
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|(-2|(1sin(2πx + 1) + 1) + 1| + 2) + 1| + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
41
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_72
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(2sin(1π((-1x + 3)/(2x - 1)) - 2) - 2) + 1| + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_73
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(-1(2cos(2πx))^2 - 4(2cos(2πx)) + 2) - 2| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
40
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_74
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2sin(2π(-3(-5x - 4) + 2) - 2) + 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
97
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_75
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(-4(1x^2 + 5x - 4)^2 - 5(1x^2 + 5x - 4) - 2) + 2| + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_76
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2(1cos(3π(5x^2 - 3x + 1)) + 3)^2 - 4(1cos(3π(5x^2 - 3x + 1)) + 3) - 4 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_77
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -4(2|(2cos(3πx + 1) + 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}"
]
}
|
61
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_78
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 2cos(3π(1(-3x + 3) + 4) + 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}"
]
}
|
90
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_79
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3sin(3π(-1|((2x - 3)/(-2x)) - 1| + 1) - 1) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_80
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(-2sin(1π(-5x - 5)) - 1) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
50
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_81
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -1sin(1π(2(1x - 4)^2 - 1(1x - 4) - 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}"
]
}
|
48
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_82
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2(1(2cos(3πx - 2))^2 - 2(2cos(3πx - 2)) + 3)^2 - 3(1(2cos(3πx - 2))^2 - 2(2cos(3πx - 2)) + 3) - 5 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
49
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_83
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(3cos(2π(-2x^2 - 1x - 1) + 3)) + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
47
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_84
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1sin(2π(-3(-3x - 4)^2 + 2(-3x - 4) + 2) - 3) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
23
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_85
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(2sin(2π(1x^2 + 3x - 5) - 1) + 3)^2 - 5(2sin(2π(1x^2 + 3x - 5) - 1) + 3) + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
22
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_86
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(-3sin(1π(-3x^2 - 4x - 5) - 2) - 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
55
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_87
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(-5(3sin(3πx))^2 + 1(3sin(3πx)) + 5)^2 - 3(-5(3sin(3πx))^2 + 1(3sin(3πx)) + 5) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
17
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_88
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(-3|(3cos(3πx - 2) - 2) + 2| + 2) + 1| + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
60
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_89
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(-5(-2cos(2πx - 3) - 3) - 2) - 2)/(-3(-5(-2cos(2πx - 3) - 3) - 2) + 1) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
21
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_90
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 5(2cos(1π((-2x - 1)/(-1x - 2)) + 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}"
]
}
|
7
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_91
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2cos(1π(-1(-4x) - 4) - 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
40
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_92
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|(-1cos(3π(-3|x + 1| - 2) - 3) + 1) + 1| + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
90
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_93
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|(-3cos(2π((1x)/(-2x - 3)) - 2) - 2) - 2| - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_94
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(1(-2sin(1πx - 1) - 3) - 4) - 3| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_95
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(4(3sin(3πx) + 3)^2 - 2(3sin(3πx) + 3) + 3) + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
16
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_96
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 2sin(1π(2|(2x^2 - 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}"
]
}
|
50
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_97
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3sin(2π(-2((-3x)/(-3x - 1))^2 - 1((-3x)/(-3x - 1))) + 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_98
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(2(1sin(2πx - 2) + 3)^2 + 4(1sin(2πx - 2) + 3) + 3) - 1)/(-2(2(1sin(2πx - 2) + 3)^2 + 4(1sin(2πx - 2) + 3) + 3) + 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
20
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_99
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2cos(1π(4(-3|x + 2| + 3)^2 - 2(-3|x + 2| + 3) - 2) + 2) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
15
|
math
|
train
|
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