messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2|(-1sin(1π(5(-3x - 4)^2 - 5(-3x - 4) + 5)) - 1) + 2| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 488 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3cos(1π(-5(-5(1x^2 - 1x + 2) + 4)^2 - 5(-5(1x^2 - 1x + 2) + 4) + 1) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 138 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 5(-2sin(1π(2|(-1|x - 3| - 2) - 2| - 3) + 3) + 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -3cos(1π(3(4(1|x - 2| - 2) - 2)^2 + 1(4(1|x - 2| - 2) - 2) + 1) - 2) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 241 | MATH |
[
{
"content": "How many local minima does the function f(x) = 5(2|(-2(-3sin(2πx - 2)) - 4) - 3| - 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 5(-4(4(-3sin(3πx + 1) + 3)^2 - 3(-3sin(3πx + 1) + 3) - 1)^2 + 4(4(-3sin(3πx + 1) + 3)^2 - 3(-3sin(3πx + 1) + 3) - 1)) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 89 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -2((2(-1(3cos(3πx) - 3)^2 + 4(3cos(3πx) - 3) + 4) + 1)/(2(-1(3cos(3πx) - 3)^2 + 4(3cos(3πx) - 3) + 4) + 2))^2 + 3((2(-1(3cos(3πx) - 3)^2 + 4(3cos(3πx) - 3) + 4) + 1)/(2(-1(3cos(3πx) - 3)^2 + 4(3cos(3πx) - 3) + 4) + 2)) + 4 have in the interval [-10, 1... | 132 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1sin(1π(-3(4(1x - 2)^2 - 4(1x - 2) - 5)) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 511 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5(1|(3|(-2sin(2πx - 1) + 2) - 3| - 3) - 3|) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 119 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (3(-3sin(1π(-2(-3|x - 2| - 2) - 3) + 1) + 1) + 3)/(-2(-3sin(1π(-2(-3|x - 2| - 2) - 3) + 1) + 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 233 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 2(3((-2(-3x^2 + 2x - 2) - 2)/(-3(-3x^2 + 2x - 2) - 3))) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (-1(1(1e^(2(1x^2 - 1x - 1)) + 2) + 4) + 2)/(-2(1(1e^(2(1x^2 - 1x - 1)) + 2) + 4) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -3(1|((-1(-1x^2 - 3x - 2) + 1)/(-3(-1x^2 - 3x - 2))) - 3| - 2)^2 - 2(1|((-1(-1x^2 - 3x - 2) + 1)/(-3(-1x^2 - 3x - 2))) - 3| - 2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 1sin(3π(3|(-3|(5x^2 + 4x - 5) + 2| + 1) + 3|) + 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 222 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -3|(2|(5(2|x + 2| - 3)^2 - 5) + 1| + 3) - 3| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2(-3sin(2π(2(5x + 3)^2 - 3(5x + 3) + 2) + 2) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 405 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 2(-1(3sin(2π(-3x^2 + 1) - 2) + 2) + 5) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 449 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 5(-1sin(3π(-2(-1x - 1)^2 + 2(-1x - 1) + 5) - 1) - 2)^2 - 5(-1sin(3π(-2(-1x - 1)^2 + 2(-1x - 1) + 5) - 1) - 2) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 267 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -2(2|(-3cos(2π(2x^2 - 1x + 1) - 2) + 3) + 2| + 3)^2 - 5(2|(-3cos(2π(2x^2 - 1x + 1) - 2) + 3) + 2| + 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 260 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2(-2e^(1(5(-1x^2 - 1x + 2)^2 - 3(-1x^2 - 1x + 2) + 4)) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(3|(1e^(-2(-1|x - 2| + 3)) + 2) - 3| - 2)^2 + 1(3|(1e^(-2(-1|x - 2| + 3)) + 2) - 3| - 2) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (-3(2cos(3π(1(-3|x - 1| + 2) - 3)) - 2) - 3)/(-2(2cos(3π(1(-3|x - 1| + 2) - 3)) - 2)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2sin(1π(1|(-1(-5x^2 + 3x + 2)^2 - 5(-5x^2 + 3x + 2) - 3) + 2| + 2) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 234 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 1e^(-1(-2(-2|(-2x^2 - 5x - 2) + 1| + 3)^2 - 3(-2|(-2x^2 - 5x - 2) + 1| + 3) + 4)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 3cos(2π(-4(-4(5x^2 + 3x + 1)^2 + 5)^2) - 2) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 1(3sin(2π(3((-3x + 3)/(-3x - 2))^2 - 1((-3x + 3)/(-3x - 2)) + 4) - 3) + 1)^2 + 3(3sin(2π(3((-3x + 3)/(-3x - 2))^2 - 1((-3x + 3)/(-3x - 2)) + 4) - 3) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 55 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 5(1|(-2sin(2π(1x^2 + 2x + 4) - 3) + 2) - 2| - 2)^2 - 3(1|(-2sin(2π(1x^2 + 2x + 4) - 3) + 2) - 2| - 2) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 563 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 2sin(1π(-1((-3(3x))/(2(3x) - 1))) + 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "How many local minima does the function f(x) = (1(-5(1(-5x^2 + 4x + 2)^2 - 4)^2 - 3) - 3)/(-3(-5(1(-5x^2 + 4x + 2)^2 - 4)^2 - 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 3sin(1π(4(1((-3x - 1)/(-2x - 2)) - 5)^2 - 2(1((-3x - 1)/(-2x - 2)) - 5) - 4)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(-1(-3|(-3sin(3πx) + 2) + 1| - 3)^2 - 1)^2 - 2(-1(-3|(-3sin(3πx) + 2) + 1| - 3)^2 - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1sin(2π(1(1|(-2x - 1) - 1| - 3) - 3) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2((-3(-2sin(2π(5x^2 - 3x - 1) + 3) + 3) + 2)/(-2(-2sin(2π(5x^2 - 3x - 1) + 3) + 3) + 3))^2 + 3((-3(-2sin(2π(5x^2 - 3x - 1) + 3) + 3) + 2)/(-2(-2sin(2π(5x^2 - 3x - 1) + 3) + 3) + 3)) - 4 in the interval [-10, 10].\n\nPresent... | 495 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1cos(1π(2|(2|((2x + 2)/(2x)) + 1| + 3) - 2| + 1) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-3(-1(2|(-2|x| - 2) - 2|) + 2))/(-2(-1(2|(-2|x| - 2) - 2|) + 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 85 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -2(1(-1e^(-1(5x^2 - 1x - 5)) - 2)^2 + 5(-1e^(-1(5x^2 - 1x - 5)) - 2) + 4)^2 - 4(1(-1e^(-1(5x^2 - 1x - 5)) - 2)^2 + 5(-1e^(-1(5x^2 - 1x - 5)) - 2) + 4) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 7 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (2(-3cos(1π((1((2x + 3)/(3x - 2)) - 3)/(2((2x + 3)/(3x - 2)) - 3)) + 3) + 3) - 3)/(-2(-3cos(1π((1((2x + 3)/(3x - 2)) - 3)/(2((2x + 3)/(3x - 2)) - 3)) + 3) + 3) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 25 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -2((3(1e^(-1(-5x^2 - 5x - 4)) + 1))/(-2(1e^(-1(-5x^2 - 5x - 4)) + 1) - 3)) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
[
{
"content": "How many local minima does the function f(x) = -2|(2(1(-2x + 5)^2 + 5(-2x + 5) - 4)^2 - 3(1(-2x + 5)^2 + 5(-2x + 5) - 4) - 4) + 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1(-3cos(3π(-3|(-2x^2 - 2x - 2) - 2| - 2) + 2) - 2)^2 - 5(-3cos(3π(-3|(-2x^2 - 2x - 2) - 2| - 2) + 2) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 276 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -3(-2(1|(1cos(3πx + 3) - 1) - 1| - 1) + 1)^2 - 1(-2(1|(1cos(3πx + 3) - 1) - 1| - 1) + 1) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2(1sin(1π((-3(-3|x + 2| + 1) + 3)/(-1(-3|x + 2| + 1) - 2)) + 2) - 3) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 62 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3|(2|(-2cos(1π(1|x - 3| + 3) + 1) + 3) - 1| + 3) + 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (-2(-2cos(3π((2(1x - 2) + 2)/(-2(1x - 2) - 1)) - 2)) + 2)/(-2(-2cos(3π((2(1x - 2) + 2)/(-2(1x - 2) - 1)) - 2)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (2(2|(1cos(3π((-2x - 1)/(2x)) + 3) - 2)| - 1) + 1)/(-2(2|(1cos(3π((-2x - 1)/(2x)) + 3) - 2)| - 1) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -1|(2(-4(-1|x - 1| + 3)^2 + 2(-1|x - 1| + 3) + 5)^2 + 1(-4(-1|x - 1| + 3)^2 + 2(-1|x - 1| + 3) + 5) + 1) + 1| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 2|(1(2|(-4x^2 - 4x - 4) + 3| + 1)^2 - 4(2|(-4x^2 - 4x - 4) + 3| + 1) + 2) - 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (-1(-1(-2|(-3|x + 1| + 3) - 1| - 1) + 5) - 1)/(3(-1(-2|(-3|x + 1| + 3) - 1| - 1) + 5) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 123 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 1(1sin(2π(1(-3|x + 2| + 3)^2 - 3) - 2) + 1)^2 - 2(1sin(2π(1(-3|x + 2| + 3)^2 - 3) - 2) + 1) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 247 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (3(-1e^(-2(3(-3x^2 + 1x) - 3)) + 2) - 2)/(1(-1e^(-2(3(-3x^2 + 1x) - 3)) + 2) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "How many local minima does the function f(x) = 2|(2cos(1π(1(-4x^2 + 2x - 5)^2 - 4(-4x^2 + 2x - 5) + 2) - 2) + 2) + 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2cos(3π(2|(-2|(-3|x + 1| - 1) + 2| + 1) + 1| - 3) - 3) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 721 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (-1(-3sin(3π(-3(-5x) - 2) + 2) - 2) - 1)/(-1(-3sin(3π(-3(-5x) - 2) + 2) - 2) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 396 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (2((-2(4(1sin(2πx + 1) - 3)^2 + 1(1sin(2πx + 1) - 3) + 1) + 1)/(-1(4(1sin(2πx + 1) - 3)^2 + 1(1sin(2πx + 1) - 3) + 1) - 1)) + 3)/(-3((-2(4(1sin(2πx + 1) - 3)^2 + 1(1sin(2πx + 1) - 3) + 1) + 1)/(-1(4(1sin(2πx + 1) - 3)^2 +... | 40 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -4(3|(1cos(2π(1|x + 2| - 3) + 2) + 1) - 3| + 2)^2 + 4(3|(1cos(2π(1|x + 2| - 3) + 2) + 1) - 3| + 2) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 3|(-2sin(1π(1(-3x^2 - 4x) - 2) - 2) + 2) + 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 279 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -3cos(1π(-2|(1(-1|x + 3| - 1)^2 - 1(-1|x + 3| - 1) - 3) - 1|) - 1) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 543 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 5(5(-1(-1sin(2πx - 2) - 3)^2 + 1(-1sin(2πx - 2) - 3) - 3)^2 - 1(-1(-1sin(2πx - 2) - 3)^2 + 1(-1sin(2πx - 2) - 3) - 3) + 4) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2(-5(1(1cos(3πx) + 1)^2 - 4(1cos(3πx) + 1) + 5) + 5)^2 - 4(-5(1(1cos(3πx) + 1)^2 - 4(1cos(3πx) + 1) + 5) + 5) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 119 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 2sin(3π(-4(-3(-2x^2 + 3x + 3)^2 - 3(-2x^2 + 3x + 3) - 4)^2 - 1(-3(-2x^2 + 3x + 3)^2 - 3(-2x^2 + 3x + 3) - 4)) - 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (3(1(4(4x^2 + 3x) - 4)^2 + 2(4(4x^2 + 3x) - 4) + 4) + 3)/(-1(1(4(4x^2 + 3x) - 4)^2 + 2(4(4x^2 + 3x) - 4) + 4) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 201 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -2|(3|(-1(-2cos(3πx) + 2) + 5) + 2| - 1)| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 5((-2(1(3x - 3)^2 + 1(3x - 3) - 4) + 1)/(1(1(3x - 3)^2 + 1(3x - 3) - 4) + 1))^2 + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 5(-5(1(3sin(3πx + 1) - 3)^2 - 3(3sin(3πx + 1) - 3) + 5)^2 - 3(1(3sin(3πx + 1) - 3)^2 - 3(3sin(3πx + 1) - 3) + 5) - 3)^2 - 2(-5(1(3sin(3πx + 1) - 3)^2 - 3(3sin(3πx + 1) - 3) + 5)^2 - 3(1(3sin(3πx + 1) - 3)^2 - 3(3sin(3πx + 1) - 3) + 5) - 3... | 25 | MATH |
[
{
"content": "How many local minima does the function f(x) = (-3((-2((-1(2cos(1πx + 1)) + 2)/(-1(2cos(1πx + 1)))))/(2((-1(2cos(1πx + 1)) + 2)/(-1(2cos(1πx + 1)))) - 1)) - 1)/(-2((-2((-1(2cos(1πx + 1)) + 2)/(-1(2cos(1πx + 1)))))/(2((-1(2cos(1πx + 1)) + 2)/(-1(2cos(1πx + 1)))) - 1)) + 1) have in the interval [-10... | 10 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -3(2(-2cos(3π(-1x^2 + 5x - 1)))^2 + 4(-2cos(3π(-1x^2 + 5x - 1))) + 5)^2 + 4(2(-2cos(3π(-1x^2 + 5x - 1)))^2 + 4(-2cos(3π(-1x^2 + 5x - 1))) + 5) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 237 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1|(1(-2cos(3π(-2x - 4)) + 3)^2 - 4(-2cos(3π(-2x - 4)) + 3) - 5) + 1| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 360 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 3(5(2cos(2π(-3x^2 - 4)) - 2) + 4)^2 - 2(5(2cos(2π(-3x^2 - 4)) - 2) + 4) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 137 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(-2|(1sin(2π(-1x^2 + 5x + 5) - 2) + 3) - 1| + 3) - 1)/(1(-2|(1sin(2π(-1x^2 + 5x + 5) - 2) + 3) - 1| + 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 427 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -3|(-5(3e^(2(-2|x| - 3)) + 1))| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 2sin(3π(3((2((1x + 1)/(3x)) + 2)/(2((1x + 1)/(3x)) - 3))^2 + 2((2((1x + 1)/(3x)) + 2)/(2((1x + 1)/(3x)) - 3)) - 5) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -2|(-3sin(3π(-2|(-1x) + 2| - 2) - 3) - 2) - 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -1sin(1π(5(1(-2|x + 1| - 3) + 4) - 2) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -1sin(1π(-3|(1|(1|x + 1| - 3) - 2| - 2) - 2| - 1) + 2) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -1|((2(1e^(2(-3x - 5)) - 1) + 2)/(2(1e^(2(-3x - 5)) - 1) - 1)) - 1| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(1(1|(-3sin(3πx + 1) + 1) - 1| + 3) - 1)^2 - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 111 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -2|(2(-4(-3cos(2πx - 1) - 2)^2 - 1(-3cos(2πx - 1) - 2) - 1) + 2) + 2| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (-2(-3sin(3π(-3(-2x^2 + 3x + 3)^2 - 5(-2x^2 + 3x + 3) + 4) + 1) + 3) - 3)/(-2(-3sin(3π(-3(-2x^2 + 3x + 3)^2 - 5(-2x^2 + 3x + 3) + 4) + 1) + 3) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 214 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 2cos(3π(-1(-2|(-4x) - 1| - 1) + 2) + 1) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 481 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1(-4(2(2cos(3πx - 1) + 1) - 1)^2 - 2(2(2cos(3πx - 1) + 1) - 1) - 4)^2 + 1(-4(2(2cos(3πx - 1) + 1) - 1)^2 - 2(2(2cos(3πx - 1) + 1) - 1) - 4) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 60 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -2|(1|(-3(-1x^2 + 1)^2 + 2(-1x^2 + 1) + 2)| + 2) + 3| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -1cos(1π(1(1(-1x + 5)^2 + 1(-1x + 5) + 2) + 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 130 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 1cos(1π(-2(-5(-1x + 5) + 3)) - 2) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1|(3((-3(-1cos(3πx + 2) - 2) - 3)/(3(-1cos(3πx + 2) - 2) - 2)) - 4)| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "How many local minima does the function f(x) = (2(2cos(1π(-5(5x - 2) - 1) + 3) + 3) - 2)/(3(2cos(1π(-5(5x - 2) - 1) + 3) + 3) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 174 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 1(-3sin(3π(4(2|x - 3| + 1) - 3) + 1) + 3) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 239 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1|(3|(3|(1sin(3πx + 3) + 1) + 2| - 3)| - 1) - 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (2(2(1sin(3π((3x + 1)/(2x - 1)) - 1))^2 - 2(1sin(3π((3x + 1)/(2x - 1)) - 1))) + 2)/(3(2(1sin(3π((3x + 1)/(2x - 1)) - 1))^2 - 2(1sin(3π((3x + 1)/(2x - 1)) - 1))) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex ... | 53 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -3|(-3sin(2π(3|(2|x - 2| - 2) - 3| - 2) + 3) + 3) + 3| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1cos(3π(5((1(-2x + 5) + 2)/(-3(-2x + 5) - 1))^2 - 3) - 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2(1e^(-2(-1(-1|x + 1| + 1)^2 + 2)) + 1)^2 - 4(1e^(-2(-1(-1|x + 1| + 1)^2 + 2)) + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 2|(-2(2sin(2π(-3x^2 - 5x - 2)) - 3)^2 - 1(2sin(2π(-3x^2 - 5x - 2)) - 3) + 5) - 3| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 469 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 3|(-3((3(-1cos(3πx + 1)) + 2)/(2(-1cos(3πx + 1)) + 3)) - 5) - 1| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -5((2(4(-1cos(3πx) + 2)^2 - 5(-1cos(3πx) + 2)) - 3)/(2(4(-1cos(3πx) + 2)^2 - 5(-1cos(3πx) + 2)) - 1))^2 - 3((2(4(-1cos(3πx) + 2)^2 - 5(-1cos(3πx) + 2)) - 3)/(2(4(-1cos(3πx) + 2)^2 - 5(-1cos(3πx) + 2)) - 1)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the a... | 36 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -1(-3(1|(-1|x - 1| + 2) + 2| + 1)^2 - 3(1|(-1|x - 1| + 2) + 2| + 1) + 5)^2 - 4(-3(1|(-1|x - 1| + 2) + 2| + 1)^2 - 3(1|(-1|x - 1| + 2) + 2| + 1) + 5) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 7 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2(-1(-2(-5x^2 + 5x - 3)^2 - 3(-5x^2 + 5x - 3) - 1)^2 - 4(-2(-5x^2 + 5x - 3)^2 - 3(-5x^2 + 5x - 3) - 1) - 3)^2 - 2(-1(-2(-5x^2 + 5x - 3)^2 - 3(-5x^2 + 5x - 3) - 1)^2 - 4(-2(-5x^2 + 5x - 3)^2 - 3(-5x^2 + 5x - 3) - 1) - 3) + 1... | 5 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (3(-1sin(2π(3((-2x - 1)/(-3x)) + 5) + 2)))/(2(-1sin(2π(3((-2x - 1)/(-3x)) + 5) + 2)) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 1(3(1(-1cos(3πx + 2) + 3)^2 + 4(-1cos(3πx + 2) + 3) + 1) - 4) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2(3sin(2π(-3|((-1x - 1)/(1x + 3)) - 1| + 1) - 3) + 2)^2 - 3(3sin(2π(-3|((-1x - 1)/(1x + 3)) - 1| + 1) - 3) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 79 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 3|(-1cos(2π(-2|(1x + 5)| - 2)) + 2)| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
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