id
stringlengths 39
39
| setting_key
stringclasses 1
value | setting_name
stringclasses 0
values | messages
listlengths 1
1
| ground_truth
stringclasses 70
values | dataset
stringclasses 1
value |
|---|---|---|---|---|---|
algebra_func_derivative_sign_train_0000
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(-1(-2cos(1πx + 2) - 3)^2 + 1(-2cos(1πx + 2) - 3) + 5) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
math
|
algebra_func_derivative_sign_train_0001
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1sin(3π((3(5x^2 - 5) + 2)/(-1(5x^2 - 5) - 2)) - 3) - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9
|
math
|
algebra_func_derivative_sign_train_0002
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = -5(2|(2cos(1π((3x - 2)/(-3x + 4)))) + 1| - 3)^2 + 5(2|(2cos(1π((3x - 2)/(-3x + 4)))) + 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}"
}
] |
5
|
math
|
algebra_func_derivative_sign_train_0003
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(1sin(2π(2|(1x^2 - 1x + 4) + 1| - 2) + 2)) - 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
50
|
math
|
algebra_func_derivative_sign_train_0004
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3sin(3π((-1(2(-4x - 5)^2 + 1(-4x - 5) + 3) + 1)/(-3(2(-4x - 5)^2 + 1(-4x - 5) + 3) - 2)) - 1) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0005
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(-2(1cos(1π((-1x + 3)/(2x - 3)) - 3)) - 4)^2 - 5(-2(1cos(1π((-1x + 3)/(2x - 3)) - 3)) - 4) + 4 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_derivative_sign_train_0006
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = (3(-2|(-4(3cos(2πx - 2) - 1)^2 + 1(3cos(2πx - 2) - 1) + 3) - 2| + 3) - 1)/(-1(-2|(-4(3cos(2πx - 2) - 1)^2 + 1(3cos(2πx - 2) - 1) + 3) - 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}"
}
] |
41
|
math
|
algebra_func_derivative_sign_train_0007
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|((2(4x^2 - 4x) - 2)/(-2(4x^2 - 4x) - 1)) + 2| - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0008
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(-3((1(-1|x - 3| + 2) - 3)/(-2(-1|x - 3| + 2)))^2 - 3((1(-1|x - 3| + 2) - 3)/(-2(-1|x - 3| + 2))) - 4) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0009
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = 2(5((-1x + 3)/(-3x + 2)) + 3)^2 - 2(5((-1x + 3)/(-3x + 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}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0010
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = -4(-3cos(1πx + 1) + 3)^2 + 5(-3cos(1πx + 1) + 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}"
}
] |
20
|
math
|
algebra_func_derivative_sign_train_0011
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = 2sin(2π(1(-1x^2 - 4x - 1) + 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}"
}
] |
55
|
math
|
algebra_func_derivative_sign_train_0012
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(1|((3(5x^2 + 5x - 4) - 3)/(-2(5x^2 + 5x - 4))) - 2| - 3) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_derivative_sign_train_0013
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3(-1|x + 1| + 2)^2 - 4(-1|x + 1| + 2) - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0014
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(1|((2(2x + 3) + 2)/(-1(2x + 3))) + 1| - 3)^2 - 1(1|((2(2x + 3) + 2)/(-1(2x + 3))) + 1| - 3) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0015
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1sin(1π(5((-1x + 3)/(-3x))^2 - 2((-1x + 3)/(-3x)) - 2) - 1) + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
algebra_func_derivative_sign_train_0016
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(-1(-1e^(1(-3|x + 1| + 2)) + 2)^2 - 2(-1e^(1(-3|x + 1| + 2)) + 2) - 3) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0017
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3(-3cos(2π(2|x - 1| + 2) - 1) + 2) - 3)/(2(-3cos(2π(2|x - 1| + 2) - 1) + 2) + 1) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
41
|
math
|
algebra_func_derivative_sign_train_0018
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(-1(2((-1x + 1)/(1x))^2 + 1((-1x + 1)/(1x)) + 2) + 3)| - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0019
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|((-1(1cos(3πx + 3) - 2) - 1)/(2(1cos(3πx + 3) - 2))) - 2| - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
31
|
math
|
algebra_func_derivative_sign_train_0020
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3cos(2π(3|((2x + 1)/(1x)) + 3| + 1) - 2) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9
|
math
|
algebra_func_derivative_sign_train_0021
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = -2cos(2π((-3(3(-3|x + 1| + 3)^2 - 1(-3|x + 1| + 3) + 2) - 1)/(1(3(-3|x + 1| + 3)^2 - 1(-3|x + 1| + 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}"
}
] |
8
|
math
|
algebra_func_derivative_sign_train_0022
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(2x^2 - 2x - 5) + 3| + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0023
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = 1cos(2π(-1(2x^2 - 2x + 4) - 4) + 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}"
}
] |
45
|
math
|
algebra_func_derivative_sign_train_0024
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = -5(-1(2sin(2π((3x - 1)/(-1x + 3)) - 1)) + 3)^2 + 4(-1(2sin(2π((3x - 1)/(-1x + 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
|
algebra_func_derivative_sign_train_0025
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = -1|(3((1x - 3)/(-2x))) + 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}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0026
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(2cos(1πx - 2) - 2) + 3)/(3(2cos(1πx - 2) - 2) + 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
algebra_func_derivative_sign_train_0027
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = 2(1|((-2(2x^2 - 4x + 2) + 2)/(-1(2x^2 - 4x + 2) + 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}"
}
] |
3
|
math
|
algebra_func_derivative_sign_train_0028
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1e^(2(-2|((-1(2x - 1) - 1)/(-2(2x - 1) + 3)) + 2| + 3)) - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0029
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2((2(-5(1|x + 3| - 2) + 3) - 3)/(3(-5(1|x + 3| - 2) + 3) + 2))^2 - 5((2(-5(1|x + 3| - 2) + 3) - 3)/(3(-5(1|x + 3| - 2) + 3) + 2)) - 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0030
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(-4(3|x| - 1) + 1)^2 + 4(-4(3|x| - 1) + 1) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0031
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3(-3cos(2πx - 1)) + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20
|
math
|
algebra_func_derivative_sign_train_0032
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = (2(-5(2sin(1πx - 1))^2 + 5(2sin(1πx - 1)) - 5))/(2(-5(2sin(1πx - 1))^2 + 5(2sin(1πx - 1)) - 5) - 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
|
algebra_func_derivative_sign_train_0033
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(2cos(2π(-2x^2 - 1x - 5) - 2) + 2) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
39
|
math
|
algebra_func_derivative_sign_train_0034
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(2|(3sin(3π(-4x^2 - 3x - 5) - 3) - 2) - 1| - 2) + 1)/(-1(2|(3sin(3π(-4x^2 - 3x - 5) - 3) - 2) - 1| - 2) - 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
48
|
math
|
algebra_func_derivative_sign_train_0035
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1sin(1π(-1x - 4) + 1) - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
math
|
algebra_func_derivative_sign_train_0036
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3cos(1π(-3|x + 1| - 1) + 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
31
|
math
|
algebra_func_derivative_sign_train_0037
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(-1(-5(1|x + 2| - 3) + 1)^2 + 2(-5(1|x + 2| - 3) + 1) - 2) - 3)/(-1(-1(-5(1|x + 2| - 3) + 1)^2 + 2(-5(1|x + 2| - 3) + 1) - 2) - 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0038
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = -2cos(3π(-1|x - 2| - 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}"
}
] |
31
|
math
|
algebra_func_derivative_sign_train_0039
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(3sin(1πx + 3) - 1) - 3)/(2(3sin(1πx + 3) - 1) + 1) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
algebra_func_derivative_sign_train_0040
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|((-2(-2x - 1) + 3)/(2(-2x - 1) - 1)) - 3| - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0041
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = 1cos(1π(-3|x - 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}"
}
] |
31
|
math
|
algebra_func_derivative_sign_train_0042
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = 1(2|(5((2x)/(2x + 2)) - 2)| - 3)^2 - 5(2|(5((2x)/(2x + 2)) - 2)| - 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}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0043
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1sin(2π(-3x - 3) + 3) - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
61
|
math
|
algebra_func_derivative_sign_train_0044
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-3(-1cos(1π(-2|(2x) + 2| - 2) - 3) + 2) + 2)/(-1(-1cos(1π(-2|(2x) + 2| - 2) - 3) + 2) - 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
math
|
algebra_func_derivative_sign_train_0045
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = -2|(2((1x + 2)/(3x + 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}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0046
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3sin(3π(4x^2 + 3x - 1) - 2) - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
37
|
math
|
algebra_func_derivative_sign_train_0047
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = -5(2sin(1π(-1|x| + 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}"
}
] |
11
|
math
|
algebra_func_derivative_sign_train_0048
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = 2cos(3π(-1((1(-5x^2 - 5x + 4) - 3)/(-1(-5x^2 - 5x + 4) - 1)) - 4) - 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}"
}
] |
10
|
math
|
algebra_func_derivative_sign_train_0049
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3sin(3π(-5(1|x + 3| + 1)^2 - 3(1|x + 3| + 1) - 3)) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
30
|
math
|
algebra_func_derivative_sign_train_0050
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = 2(3(2e^(-1(2|x - 2| - 1)) - 3))^2 - 3(3(2e^(-1(2|x - 2| - 1)) - 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}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0051
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2sin(1π(-1(3|x + 3| - 2)^2 - 5(3|x + 3| - 2) + 1) + 3) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
50
|
math
|
algebra_func_derivative_sign_train_0052
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = -1|((-3(3(3x - 1)^2 + 1(3x - 1) - 4) - 3)/(1(3(3x - 1)^2 + 1(3x - 1) - 4) - 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}"
}
] |
3
|
math
|
algebra_func_derivative_sign_train_0053
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(1cos(2πx + 1) + 2) - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
21
|
math
|
algebra_func_derivative_sign_train_0054
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(-3|x - 1| + 1)^2 + 5(-3|x - 1| + 1) + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0055
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(1(3|(-2e^(1x) + 3) - 1| - 2)^2 - 2(3|(-2e^(1x) + 3) - 1| - 2) + 4) - 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0056
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(1((1(3sin(2πx - 3) - 3) + 3)/(1(3sin(2πx - 3) - 3)))^2 + 3((1(3sin(2πx - 3) - 3) + 3)/(1(3sin(2πx - 3) - 3))) - 1) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
23
|
math
|
algebra_func_derivative_sign_train_0057
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = 1sin(1π(1(1(-2|x - 3| - 3)^2 - 2(-2|x - 3| - 3) + 4) + 4) + 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}"
}
] |
46
|
math
|
algebra_func_derivative_sign_train_0058
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(2cos(1πx - 1) - 2) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
math
|
algebra_func_derivative_sign_train_0059
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3((3x + 2)/(-2x + 3))^2 + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0060
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|(-2((-2(3x^2 - 1))/(2(3x^2 - 1) - 3)) - 5) + 1| positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_derivative_sign_train_0061
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = -1cos(1π(3((1x - 2)/(-3x - 1))^2 + 5((1x - 2)/(-3x - 1)) + 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}"
}
] |
8
|
math
|
algebra_func_derivative_sign_train_0062
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = -1|(-5((3(4x + 2) + 1)/(-1(4x + 2) - 2))^2 - 5((3(4x + 2) + 1)/(-1(4x + 2) - 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}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0063
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(1|(-1cos(2πx - 3) - 1)|) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
21
|
math
|
algebra_func_derivative_sign_train_0064
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = 3(-3(-3cos(3πx + 1) + 1) + 1)^2 + 2(-3(-3cos(3πx + 1) + 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}"
}
] |
15
|
math
|
algebra_func_derivative_sign_train_0065
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1sin(3π(-2|x| + 3) + 2) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
60
|
math
|
algebra_func_derivative_sign_train_0066
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = 1(-3e^(1(-2((2x + 2)/(-3x + 2)) + 3)) + 1)^2 + 2(-3e^(1(-2((2x + 2)/(-3x + 2)) + 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}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0067
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = 1sin(3π(5((-1x)/(-3x - 2)) - 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}"
}
] |
9
|
math
|
algebra_func_derivative_sign_train_0068
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = 2cos(1π(-2x^2 + 1x - 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}"
}
] |
46
|
math
|
algebra_func_derivative_sign_train_0069
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2(1(-2|x + 1| + 3)^2 - 5(-2|x + 1| + 3) - 5) - 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0070
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = 3|(5(3sin(1πx + 1) + 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}"
}
] |
21
|
math
|
algebra_func_derivative_sign_train_0071
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1cos(1π((-3(-5(-1x^2 + 4x - 5) - 5) - 1)/(3(-5(-1x^2 + 4x - 5) - 5) - 1)) - 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_derivative_sign_train_0072
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(2(-2((1x + 3)/(-2x + 3)) + 1)^2 - 5)| + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_derivative_sign_train_0073
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = 1|(-5(-3x^2 - 4x + 4) - 4) - 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}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0074
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(-3cos(3πx + 2))^2 + 5(-3cos(3πx + 2)) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
60
|
math
|
algebra_func_derivative_sign_train_0075
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (3(2|(-1x^2 - 4x + 1) - 2| - 3))/(-1(2|(-1x^2 - 4x + 1) - 2| - 3) - 1) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0076
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = (2(2|(3x^2 - 4) + 2| - 1) + 2)/(-1(2|(3x^2 - 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}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0077
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(-2cos(1πx + 2) - 1)^2 - 4(-2cos(1πx + 2) - 1) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
21
|
math
|
algebra_func_derivative_sign_train_0078
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2((3(-1|x + 1| + 3) + 3)/(-1(-1|x + 1| + 3)))^2 + 1((3(-1|x + 1| + 3) + 3)/(-1(-1|x + 1| + 3))) - 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_derivative_sign_train_0079
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(-3sin(2πx + 1) - 2) + 5 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
21
|
math
|
algebra_func_derivative_sign_train_0080
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = -2sin(1π(3((-2(-1x - 1) + 3)/(1(-1x - 1) + 1))^2 + 3((-2(-1x - 1) + 3)/(1(-1x - 1) + 1)) + 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}"
}
] |
20
|
math
|
algebra_func_derivative_sign_train_0081
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|(5x^2 + 4x) - 1| - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0082
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(-4(3cos(2π(2|x - 1| + 1) + 2) + 3)^2 - 1(3cos(2π(2|x - 1| + 1) + 2) + 3) - 3) + 3)/(2(-4(3cos(2π(2|x - 1| + 1) + 2) + 3)^2 - 1(3cos(2π(2|x - 1| + 1) + 2) + 3) - 3) - 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
41
|
math
|
algebra_func_derivative_sign_train_0083
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1((1(-2cos(3πx)) + 2)/(3(-2cos(3πx)) - 1))^2 + 5((1(-2cos(3πx)) + 2)/(3(-2cos(3πx)) - 1)) + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
34
|
math
|
algebra_func_derivative_sign_train_0084
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = 5(-3sin(1π((3x + 1)/(2x - 3)) - 3) - 1)^2 + 5(-3sin(1π((3x + 1)/(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}"
}
] |
8
|
math
|
algebra_func_derivative_sign_train_0085
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(1|(-1(1cos(3πx) + 1) + 2) + 2|)^2 + 3(1|(-1(1cos(3πx) + 1) + 2) + 2|) + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
30
|
math
|
algebra_func_derivative_sign_train_0086
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3e^(-1(-5(3x + 3)^2 + 2(3x + 3) - 1)) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0087
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = (-3(5(-2|(-1x + 4) - 1| + 2)^2 + 2(-2|(-1x + 4) - 1| + 2) + 5) + 1)/(-1(5(-2|(-1x + 4) - 1| + 2)^2 + 2(-2|(-1x + 4) - 1| + 2) + 5) + 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}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0088
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = (2(1cos(2π(3|x|) - 3) + 3) - 2)/(2(1cos(2π(3|x|) - 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}"
}
] |
61
|
math
|
algebra_func_derivative_sign_train_0089
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(-1(5((3x - 3)/(-2x - 2))^2 + 1((3x - 3)/(-2x - 2)) - 2) - 5) + 1| is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0090
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3sin(3π(5((-2x + 1)/(-2x + 3))^2 - 4((-2x + 1)/(-2x + 3)) - 1) - 3) - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
16
|
math
|
algebra_func_derivative_sign_train_0091
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1((-3(-3sin(1πx)) + 3)/(-1(-3sin(1πx)) + 3))^2 + 5 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20
|
math
|
algebra_func_derivative_sign_train_0092
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(2cos(2πx) - 1) - 3| + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20
|
math
|
algebra_func_derivative_sign_train_0093
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = 1sin(2π((2(4x))/(-1(4x) + 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}"
}
] |
5
|
math
|
algebra_func_derivative_sign_train_0094
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(1(1(-1|x + 2|)^2 + 2(-1|x + 2|) + 1) + 2) - 3)/(-1(1(1(-1|x + 2|)^2 + 2(-1|x + 2|) + 1) + 2) - 1) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0095
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = (1(1(5(-1|x + 2| + 1)^2 - 5(-1|x + 2| + 1) + 5) + 5) + 3)/(2(1(5(-1|x + 2| + 1)^2 - 5(-1|x + 2| + 1) + 5) + 5) - 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}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0096
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(-1(-1cos(1π(-1|x - 1| + 1) + 3) - 2) - 4)^2 + 4(-1(-1cos(1π(-1|x - 1| + 1) + 3) - 2) - 4) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
algebra_func_derivative_sign_train_0097
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(4x^2 + 3x + 2) - 3| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0098
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "For the function f(x) = -3|(-5(1e^(2(-1x)) - 1)^2 - 4(1e^(2(-1x)) - 1) + 5)| - 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}"
}
] |
2
|
math
|
algebra_func_derivative_sign_train_0099
|
algebra_func_derivative_sign
| null |
[
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(2cos(1π(3(-3|x + 1|)^2 + 1(-3|x + 1|) + 2) - 3) + 2))/(3(2cos(1π(3(-3|x + 1|)^2 + 1(-3|x + 1|) + 2) - 3) + 2) + 1) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
math
|
End of preview. Expand
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