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_200
|
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((2(3sin(1πx - 2) + 3))/(1(3sin(1πx - 2) + 3) - 3))^2 - 3((2(3sin(1πx - 2) + 3))/(1(3sin(1πx - 2) + 3) - 3)) - 5 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
20
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_201
|
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(3|x - 2| - 2)^2 - 5(3|x - 2| - 2) + 3) + 1| - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_202
|
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(-5(3sin(2πx - 3) - 3) + 1)^2 + 2(-5(3sin(2πx - 3) - 3) + 1) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
20
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_203
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 4(3sin(1π(-5x - 1) - 2) + 3)^2 + 2(3sin(1π(-5x - 1) - 2) + 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}"
]
}
|
50
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_204
|
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(2π(-5(1x^2 - 3x + 1) + 3) - 1) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
63
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_205
|
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(1π(-1(-1x^2 - 4x - 3) + 1) - 3) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
50
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_206
|
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(2(-3cos(2πx - 3) - 1)^2 + 3(-3cos(2πx - 3) - 1) + 1)^2 + 2(2(-3cos(2πx - 3) - 1)^2 + 3(-3cos(2πx - 3) - 1) + 1) - 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
17
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_207
|
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|(3sin(1π((-2x + 3)/(1x + 2)) - 1) + 1) + 3| + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_208
|
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(3π(3|(-1x^2 + 4x - 1) - 2|) - 2) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
49
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_209
|
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(3π(3((3x - 3)/(3x - 1))^2 - 2((3x - 3)/(3x - 1)) - 4) + 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_210
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 3sin(1π(-3(-4x^2 - 5x + 5)^2 + 1(-4x^2 - 5x + 5) + 5) - 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}"
]
}
|
7
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_211
|
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(2cos(1π((1x + 3)/(1x)) - 3) - 2)^2 - 2(2cos(1π((1x + 3)/(1x)) - 3) - 2) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_212
|
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(3sin(1πx + 3) + 1))/(-2(3sin(1πx + 3) + 1) + 3)) + 3)/(-2((1(3sin(1πx + 3) + 1))/(-2(3sin(1πx + 3) + 1) + 3)) - 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_213
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 1sin(2π(-2(2x^2 + 3x)^2 + 4(2x^2 + 3x) - 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}"
]
}
|
10
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_214
|
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(-3cos(1π(3|x + 1| - 2) - 3) - 1)^2 + 3(-3cos(1π(3|x + 1| - 2) - 3) - 1) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
61
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_215
|
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(2π(-1|(-2|x| - 3) - 1|) - 3) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
40
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_216
|
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(-3sin(1πx - 2) - 3) - 2)/(-2(-3sin(1πx - 2) - 3) - 1)) - 1| - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
21
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_217
|
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(-2(2cos(1πx + 2) + 2)^2 + 2(2cos(1πx + 2) + 2) + 1)^2 - 4(-2(2cos(1πx + 2) + 2)^2 + 2(2cos(1πx + 2) + 2) + 1) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
31
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_218
|
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(2sin(1π((1x + 2)/(-1x - 3)) + 2) - 1)^2 + 2(2sin(1π((1x + 2)/(-1x - 3)) + 2) - 1) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_219
|
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(3π(-5x^2 - 2) - 3) - 2) - 3| + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
18
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_220
|
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((3x - 1)/(-1x + 2)) + 1) - 2))/(-2(2sin(1π((3x - 1)/(-1x + 2)) + 1) - 2) - 2) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_221
|
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((-2x + 1)/(-3x))^2 - 1((-2x + 1)/(-3x)) - 3) - 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_222
|
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(2cos(1πx - 1) + 3))/(-3(2cos(1πx - 1) + 3) - 1)) - 2)/(2((3(2cos(1πx - 1) + 3))/(-3(2cos(1πx - 1) + 3) - 1))) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_223
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 2|(2(3sin(3πx - 1) + 1)^2 + 5(3sin(3πx - 1) + 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}"
]
}
|
44
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_224
|
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(2sin(1π((3x - 1)/(2x + 2)) + 2) + 2) - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_225
|
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(1π((-2x - 2)/(-3x + 2)) - 1) + 3) + 2)/(1(-2cos(1π((-2x - 2)/(-3x + 2)) - 1) + 3) - 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_226
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 1cos(3π(-5(-4x^2 - 2x + 3) + 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}"
]
}
|
28
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_227
|
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(2cos(2π(-3|x| + 3) + 2) + 3) - 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
61
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_228
|
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(2|x| - 1)^2 - 2(2|x| - 1) - 3)^2 + 4(4(2|x| - 1)^2 - 2(2|x| - 1) - 3) + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_229
|
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(2π(-4x^2 + 1x - 5)) + 3) + 2| + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
52
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_230
|
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(-4(2|x - 1| - 2) + 4) + 3) - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
81
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_231
|
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(3π(-1(1x^2 + 1x)^2 + 3(1x^2 + 1x) + 5) - 2) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
25
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_232
|
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(3|x - 2| - 1) - 2)))/(-1(-1cos(3π(3|x - 2| - 1) - 2)) - 2) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
91
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_233
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 2sin(2π((2((1x + 2)/(1x - 2)) + 2)/(-2((1x + 2)/(1x - 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}"
]
}
|
20
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_234
|
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(3π(3((-3x)/(2x + 2))^2 - 2((-3x)/(2x + 2)) - 5) + 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_235
|
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((1(-3cos(3πx + 3) + 1) + 2)/(3(-3cos(3πx + 3) + 1) + 3)) - 4 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
30
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_236
|
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(3sin(2π(-3|x - 1|) - 3) - 3)^2 + 4(3sin(2π(-3|x - 1|) - 3) - 3) - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
28
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_237
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -1|(1|(4x^2 + 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}"
]
}
|
4
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_238
|
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(3π((-1(-2|x - 1| + 2) + 1)/(3(-2|x - 1| + 2) + 3)) - 1) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_239
|
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(3π(1(2|x + 2| - 2)^2 + 4(2|x + 2| - 2) - 1) + 2) - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
36
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_240
|
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(-3|(3cos(1πx + 2) - 3) - 2| - 2)^2 - 3(-3|(3cos(1πx + 2) - 3) - 2| - 2) + 4 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_241
|
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(-5x^2 + 1x + 3)^2 + 5(-5x^2 + 1x + 3) + 3) - 3) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_242
|
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(-1|(3|x + 2| + 1) + 3|) - 1) - 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_243
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -3|(1|(-3cos(2πx - 3) + 1) + 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}"
]
}
|
41
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_244
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 3sin(2π(-2|((1x - 3)/(3x + 2)) + 3| + 2)) + 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_245
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -3sin(3π((-1(1x - 5) - 2)/(-2(1x - 5))) - 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}"
]
}
|
7
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_246
|
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(1π((3(4x - 5) + 1)/(1(4x - 5))) - 1) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_247
|
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(-5(3x^2 - 2x - 1) + 5) - 2) - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
28
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_248
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -4(2sin(3π(-5x^2 + 5x) - 1) - 1)^2 + 3(2sin(3π(-5x^2 + 5x) - 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}"
]
}
|
12
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_249
|
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|(-5(2sin(1πx + 2) - 1) - 1) + 2| + 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_250
|
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(-3cos(1π(-4x^2 - 5x + 5) - 2) + 3) - 1)/(-2(-3cos(1π(-4x^2 - 5x + 5) - 2) + 3) + 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
42
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_251
|
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(5x^2 + 3x - 4) - 5) - 1) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_252
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 2sin(2π(2|(2|x + 2| - 1) + 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}"
]
}
|
81
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_253
|
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(1π((-3(-1x) + 1)/(-1(-1x) - 3)) - 3) + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
16
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_254
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -1|(1|(-4x^2 - 4x + 4) + 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}"
]
}
|
4
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_255
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 3|(-1|(-2sin(1πx - 3) - 1) - 3| + 3) - 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}"
]
}
|
10
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_256
|
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(1π(3|(-3|x - 1| + 3)| - 2)) + 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
92
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_257
|
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(3π((1(-3x^2 - 2x + 1) - 3)/(-2(-3x^2 - 2x + 1))) + 1) + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_258
|
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(-3sin(1πx - 1) - 2)^2 - 4(-3sin(1πx - 1) - 2) - 4) - 1| - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
30
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_259
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 2cos(2π(-2(-1x^2 + 1x + 3)^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}"
]
}
|
17
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_260
|
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(-2(-3sin(3πx - 3) + 2)^2 - 2(-3sin(3πx - 3) + 2) + 5) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
26
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_261
|
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(-1|x + 2| - 3) - 1) - 1) - 4 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
31
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_262
|
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(3π(1(-1x + 5) - 1) - 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
30
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_263
|
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(-2|(-3|x + 2| + 2)| + 2)^2 - 3(-2|(-3|x + 2| + 2)| + 2) + 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_264
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = (-1(2|(3cos(3πx + 2) + 3)| - 3) + 3)/(-2(2|(3cos(3πx + 2) + 3)| - 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}"
]
}
|
31
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_265
|
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|(2sin(3π(4x^2 + 1x - 5) - 2)) - 2| + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
23
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_266
|
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(-2sin(3πx + 3) + 3) - 1)/(-2(-2sin(3πx + 3) + 3) + 3)) + 2)/(2((1(-2sin(3πx + 3) + 3) - 1)/(-2(-2sin(3πx + 3) + 3) + 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_267
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 3|(2|(-2cos(1πx - 3) - 2) - 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}"
]
}
|
11
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_268
|
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(3π(4((-3x - 1)/(-1x + 2)) + 1) - 2) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
29
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_269
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 1cos(2π((-3(5x^2 + 2x + 5) + 1)/(1(5x^2 + 2x + 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}"
]
}
|
4
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_270
|
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(2|x + 3| - 3)^2 + 3(2|x + 3| - 3) + 4) - 3| + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_271
|
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(1sin(1π(1|x + 1|)) + 3) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_272
|
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((-1(-1cos(2πx + 1)) - 1)/(-2(-1cos(2πx + 1)) - 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_273
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -1|(5(-1cos(1πx - 3)) - 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}"
]
}
|
21
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_274
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 1(2cos(3π((-2x + 1)/(1x + 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}"
]
}
|
13
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_275
|
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(1|(-1sin(1πx + 3) + 3) + 1| + 3) + 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_276
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 1cos(3π(2|((-2x - 2)/(3x + 2)) + 2| - 2) + 2) + 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}"
]
}
|
5
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_277
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = (-3(-1sin(3π(1x^2 + 2x - 3) - 1)) + 3)/(2(-1sin(3π(1x^2 + 2x - 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}"
]
}
|
38
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_278
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -2(-2sin(3π(2|x|) + 1) + 1)^2 - 2(-2sin(3π(2|x|) + 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}"
]
}
|
62
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_279
|
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(-5(1|x - 1| - 1) - 2) + 3) - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
99
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_280
|
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(3π((-1x - 2)/(1x)) - 3) - 3) - 1| - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
13
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_281
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -2|(-4(2sin(3πx) - 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}"
]
}
|
61
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_282
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -2|(2sin(2π((-3x - 2)/(2x)) - 3) - 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}"
]
}
|
6
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_283
|
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|(-2sin(2πx)) + 2| - 2) + 2)/(-2(-3|(-2sin(2πx)) + 2| - 2) + 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
20
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_284
|
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(-1x^2 + 4x - 2)^2 + 4) - 3| + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_285
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -3cos(2π(3(-1x + 4)) - 2) - 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}"
]
}
|
60
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_286
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = (-2(2|(3cos(3πx) - 3)| - 1) - 3)/(-1(2|(3cos(3πx) - 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}"
]
}
|
30
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_287
|
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(-5(-2cos(2πx + 3) + 1) + 5) + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
21
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_288
|
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(2sin(3πx) + 2))/(-1(2sin(3πx) + 2) + 3)) - 2| - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
70
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_289
|
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(-3sin(2π((1x + 1)/(1x)) - 1) - 2) - 1)/(-1(-3sin(2π((1x + 1)/(1x)) - 1) - 2)) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_290
|
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(-3cos(1π((-2x + 2)/(-1x - 2)) + 1) + 3)^2 - 3(-3cos(1π((-2x + 2)/(-1x - 2)) + 1) + 3) - 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_291
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 2(2sin(3π(-1x^2 - 1x + 4) - 2) + 3)^2 - 1(2sin(3π(-1x^2 - 1x + 4) - 2) + 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}"
]
}
|
24
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_292
|
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(3π(5(5x^2 + 2x + 2)^2 + 1(5x^2 + 2x + 2) + 4)) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_293
|
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(-4(-1cos(1πx + 2))^2 - 3(-1cos(1πx + 2)) + 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
20
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_294
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -2(-1(2cos(1πx - 3) - 1) + 3)^2 + 1(-1(2cos(1πx - 3) - 1) + 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}"
]
}
|
10
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_295
|
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(-3|(-2cos(3πx - 1) + 3) + 3| - 3)^2 + 1(-3|(-2cos(3πx - 1) + 3) + 3| - 3) - 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_296
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = -1((3(-2sin(3πx + 3) - 1) - 1)/(-2(-2sin(3πx + 3) - 1) - 1))^2 + 2((3(-2sin(3πx + 3) - 1) - 1)/(-2(-2sin(3πx + 3) - 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}"
]
}
|
37
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_297
|
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(3sin(1π(1x - 3) - 2) + 1) - 3)/(-2(3sin(1π(1x - 3) - 2) + 1) - 2) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_298
|
algebra_func_derivative_sign2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"For the function f(x) = 1(-1cos(3π(2|x - 3| + 1) + 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}"
]
}
|
60
|
math
|
train
|
math_algebra_func_derivative_sign_level_2_2_299
|
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(4(1cos(2πx + 1) - 1)^2 + 5(1cos(2πx + 1) - 1) - 3)^2 - 1(4(1cos(2πx + 1) - 1)^2 + 5(1cos(2πx + 1) - 1) - 3) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
60
|
math
|
train
|
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