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) = -4(1sin(2π(2|(-3x^2 - 4x + 5) - 1| - 3) - 3) - 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 487 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1cos(1π((-1(-3|(3x^2 - 3x + 3) - 3| + 2) + 3)/(2(-3|(3x^2 - 3x + 3) - 3| + 2) + 1)) - 2) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (2(1|(-2e^(-2(-4x^2 - 1)) - 2) + 3| - 3))/(3(1|(-2e^(-2(-4x^2 - 1)) - 2) + 3| - 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 2sin(3π(-2(-1|(-3|x - 1| - 2) - 2|)^2 + 3(-1|(-3|x - 1| - 2) - 2|) - 3) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 454 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 2(-2cos(2π(3(-2x - 2) + 2) - 2) - 1) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 1sin(2π(-3(3|((-2x)/(2x - 1))| - 3)^2 + 1(3|((-2x)/(2x - 1))| - 3) - 5) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2e^(2(-4(-2((1x - 3)/(2x + 3)) + 1) + 4)) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 2(5(-1cos(2π(5x^2 - 2) - 2) + 2) - 1)^2 - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 477 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = (1((1(1(-2sin(2πx - 3) - 2) - 3) + 1)/(3(1(-2sin(2πx - 3) - 2) - 3) + 2)) - 3)/(2((1(1(-2sin(2πx - 3) - 2) - 3) + 1)/(3(1(-2sin(2πx - 3) - 2) - 3) + 2)) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 20 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 5(-2sin(3π(-1|(2|x - 1| - 2) + 1| + 1) - 1) - 2)^2 + 5(-2sin(3π(-1|(2|x - 1| - 2) + 1| + 1) - 1) - 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 122 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -4(-1sin(2π(2|(-5x - 3) + 1| + 3) - 2) + 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 399 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (-1(1(5(3sin(1πx - 2) - 3) - 2)) + 3)/(-3(1(5(3sin(1πx - 2) - 3) - 2)) + 4) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -1|(5(1cos(3π(2|x| - 3) + 2) + 2) - 2)| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -2(-5(-2cos(1π((2x + 2)/(2x)) + 2) + 2)^2 - 4(-2cos(1π((2x + 2)/(2x)) + 2) + 2) + 1) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1|((2(-2cos(2π(-3x - 3) + 2) - 2) - 2)/(-3(-2cos(2π(-3x - 3) + 2) - 2))) - 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many local minima does the function f(x) = 3(1(-2cos(2π((3x + 3)/(1x)) - 1) + 3)^2 + 1(-2cos(2π((3x + 3)/(1x)) - 1) + 3) + 3)^2 + 4(1(-2cos(2π((3x + 3)/(1x)) - 1) + 3)^2 + 1(-2cos(2π((3x + 3)/(1x)) - 1) + 3) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxe... | 29 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1(3sin(2π((1(-2|x + 3| - 1) - 2)/(1(-2|x + 3| - 1))) - 1) + 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1((3(2(1cos(3πx + 3)) + 1) + 2)/(1(2(1cos(3πx + 3)) + 1)))^2 - 4((3(2(1cos(3πx + 3)) + 1) + 2)/(1(2(1cos(3πx + 3)) + 1))) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (-1(3|((-1(-4x^2 - 2x + 1) + 2)/(2(-4x^2 - 2x + 1))) + 3| - 3) - 2)/(-1(3|((-1(-4x^2 - 2x + 1) + 2)/(2(-4x^2 - 2x + 1))) + 3| - 3) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 5 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1(-3|(3(-1sin(3πx + 1) + 3)^2 + 4(-1sin(3πx + 1) + 3) - 1) - 3| - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 3(3sin(3π((3(-4x + 3))/(1(-4x + 3) + 1)) - 2) + 3)^2 + 1(3sin(3π((3(-4x + 3))/(1(-4x + 3) + 1)) - 2) + 3) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (-2(-4(-2cos(2π(1|x + 2| + 2) + 3) - 2) - 5) + 3)/(-1(-4(-2cos(2π(1|x + 2| + 2) + 3) - 2) - 5) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (-2((-2(3(2cos(2πx - 2))^2 - 3(2cos(2πx - 2)) + 1) + 1)/(1(3(2cos(2πx - 2))^2 - 3(2cos(2πx - 2)) + 1) + 2)) + 3)/(-3((-2(3(2cos(2πx - 2))^2 - 3(2cos(2πx - 2)) + 1) + 1)/(1(3(2cos(2πx - 2))^2 - 3(2cos(2πx - 2)) + 1) + 2)) - 1) where -10 ≤ x ≤ 10.\n... | 40 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (1(-1cos(3π((1(-1x) + 2)/(-2(-1x) + 3)) + 3) + 1) + 2)/(2(-1cos(3π((1(-1x) + 2)/(-2(-1x) + 3)) + 3) + 1) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (1(3cos(2π(-1(2|x + 1|)^2 + 5(2|x + 1|) - 5) - 1) + 2) - 2)/(-3(3cos(2π(-1(2|x + 1|)^2 + 5(2|x + 1|) - 5) - 1) + 2)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 278 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (-1(-2|((-1(1cos(2πx + 3) + 2) - 3)/(2(1cos(2πx + 3) + 2) - 1)) - 1| + 1) + 1)/(-2(-2|((-1(1cos(2πx + 3) + 2) - 3)/(2(1cos(2πx + 3) + 2) - 1)) - 1| + 1) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: ... | 40 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(-5(3sin(1π(-2x) + 3) + 1)^2 - 1(3sin(1π(-2x) + 3) + 1) - 3) + 1)/(-1(-5(3sin(1π(-2x) + 3) + 1)^2 - 1(3sin(1π(-2x) + 3) + 1) - 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your... | 80 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -3sin(3π(1(-1|((1x - 1)/(-3x - 2)) + 3| - 2) + 3) - 3) where -10 ≤ x ≤ 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) = 3|(-5(-1cos(2π(5x + 3) + 2) - 3) + 2)| have in the interval [-10, 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) = 3cos(1π(-1|((2(-5x^2 - 3x - 1) + 3)/(-1(-5x^2 - 3x - 1) - 1)) + 3| - 2) + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (-3(3(-2(-2sin(1πx) + 1) + 3)^2 + 5(-2(-2sin(1πx) + 1) + 3)))/(3(3(-2(-2sin(1πx) + 1) + 3)^2 + 5(-2(-2sin(1πx) + 1) + 3)) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -2cos(3π((-1(2|(4x + 1) - 2|) - 3)/(-2(2|(4x + 1) - 2|) - 1))) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2cos(2π((3(1|(4x + 1) + 3|) - 1)/(2(1|(4x + 1) + 3|) - 1)) + 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 1cos(3π(5(3|(-2|x + 3| - 1) + 1| - 3)^2 - 4(3|(-2|x + 3| - 1) + 1| - 3) + 4)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 172 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -3(-1(-3|(1cos(1πx - 3)) - 3| + 3)^2 + 3(-3|(1cos(1πx - 3)) - 3| + 3) + 5)^2 - 5(-1(-3|(1cos(1πx - 3)) - 3| + 3)^2 + 3(-3|(1cos(1πx - 3)) - 3| + 3) + 5) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 10 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -2(-2(3cos(3π(2x^2 + 4x - 1) + 3)) + 3)^2 - 1(-2(3cos(3π(2x^2 + 4x - 1) + 3)) + 3) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 449 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -1e^(-2(-4(-1|(-3x - 1) - 3|)^2 - 2(-1|(-3x - 1) - 3|) + 2)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -2(5(1|(-3sin(1πx + 3)) - 1| - 3)^2 + 3(1|(-3sin(1πx + 3)) - 1| - 3) + 4) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1|(-1sin(3π(-2(-2x - 5)^2 - 5(-2x - 5))) + 3)| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 505 | MATH |
[
{
"content": "How many local minima does the function f(x) = 2(1cos(1π(1(-1x^2 - 4x)^2 + 1(-1x^2 - 4x) + 2)) + 2)^2 + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 185 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -3(-4(1|(3|x + 2|) - 3| - 3) + 3)^2 - 1(-4(1|(3|x + 2|) - 3| - 3) + 3) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2|(1cos(1π((-2((-2x + 2)/(1x)) + 2)/(-1((-2x + 2)/(1x)) + 2)) + 1) + 2) - 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1sin(2π(-1(-3((3x + 1)/(-1x + 3))^2 + 4)^2 - 3(-3((3x + 1)/(-1x + 3))^2 + 4) + 2)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 184 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (-1(3cos(3π(-1|((1x - 1)/(-3x - 3))| + 1) + 2)) + 1)/(-3(3cos(3π(-1|((1x - 1)/(-3x - 3))| + 1) + 2)) + 4) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (1((1(1|(-3cos(2πx - 3) + 1) + 2| - 1) - 1)/(-3(1|(-3cos(2πx - 3) + 1) + 2| - 1))))/(3((1(1|(-3cos(2πx - 3) + 1) + 2| - 1) - 1)/(-3(1|(-3cos(2πx - 3) + 1) + 2| - 1))) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: ... | 20 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 2sin(2π((-2(-2|(1x - 3) - 1| + 1) - 3)/(-3(-2|(1x - 3) - 1| + 1) - 2)) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3e^(2(5(4((-2x + 1)/(2x + 2))^2 + 1((-2x + 1)/(2x + 2)) - 3) - 2)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -5(3|(1cos(3π(1x^2 - 2x + 1)) + 3) - 2| + 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 287 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 2(-2|(3|((1x - 1)/(-2x - 1)) + 1| + 2) - 2| + 2)^2 + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (2(-3(-5(-3cos(3πx + 3) - 2) + 3) + 1))/(-1(-3(-5(-3cos(3πx + 3) - 2) + 3) + 1) + 3) where -10 ≤ x ≤ 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) = -1cos(1π(3(3(2x^2 + 5x + 3)^2 + 2(2x^2 + 5x + 3) - 3) + 2) + 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 93 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -4(3(-1cos(1π((-3x + 2)/(-3x))) + 2) - 1)^2 + 5(3(-1cos(1π((-3x + 2)/(-3x))) + 2) - 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (3(-1|(-3sin(2π(3x - 5) - 3) - 1) - 3| - 2) + 2)/(2(-1|(-3sin(2π(3x - 5) - 3) - 1) - 3| - 2) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 3sin(3π(1|((3((-2x + 1)/(-2x + 3)) + 3)/(-3((-2x + 1)/(-2x + 3)) - 2)) + 1| - 2) + 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1(2(2sin(3π(-4x^2 - 2x + 4) + 1) - 2) - 2)^2 - 5(2(2sin(3π(-4x^2 - 2x + 4) + 1) - 2) - 2) - 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) = -2(1|(1(3sin(2πx - 3) - 1) + 2) + 2| + 2)^2 - 1(1|(1(3sin(2πx - 3) - 1) + 2) + 2| + 2) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -1|(2|(1(-3|x + 1| - 2)^2 + 5(-3|x + 1| - 2) - 3)| - 1) + 3| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 3cos(3π((1(1(-5x + 1)))/(3(1(-5x + 1)) + 3)) + 1) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1(-1cos(2π(2(1x + 5)^2 + 4(1x + 5) - 2) - 1) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 425 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1((2(4(-2sin(3πx + 1) - 3)^2 + 5(-2sin(3πx + 1) - 3) + 5))/(3(4(-2sin(3πx + 1) - 3)^2 + 5(-2sin(3πx + 1) - 3) + 5) - 1))^2 - 4((2(4(-2sin(3πx + 1) - 3)^2 + 5(-2sin(3πx + 1) - 3) + 5))/(3(4(-2sin(3πx + 1) - 3)^2 + 5(-2sin(3πx + 1) - 3) + 5... | 60 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (2((1(-2cos(1π(-1x + 2) + 3)) + 1)/(2(-2cos(1π(-1x + 2) + 3)))))/(2((1(-2cos(1π(-1x + 2) + 3)) + 1)/(2(-2cos(1π(-1x + 2) + 3)))) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5((3(-4(3cos(3πx + 2) + 3) - 3) + 3)/(-2(-4(3cos(3πx + 2) + 3) - 3) - 1))^2 - 3((3(-4(3cos(3πx + 2) + 3) - 3) + 3)/(-2(-4(3cos(3πx + 2) + 3) - 3) - 1)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex fo... | 60 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -1sin(1π((-2(2|((-3x - 3)/(3x - 2)) + 3|) + 2)/(-2(2|((-3x - 3)/(3x - 2)) + 3|) + 3)) + 3) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -4(-3sin(1π(5(1|x + 2| + 1) + 2) + 2) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -3|((-3(-3cos(1π(3|x| + 3) + 1) - 3) - 1)/(-2(-3cos(1π(3|x| + 3) + 1) - 3) - 3)) - 3| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4(-1|(3(-4x^2 + 5x + 3)^2 + 4(-4x^2 + 5x + 3) - 3) + 3| - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -1(1cos(3π(-2|(-3x - 5)| - 1) + 3) + 3)^2 - 3(1cos(3π(-2|(-3x - 5)| - 1) + 3) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 361 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2(-1|(1(3sin(2πx + 2) + 3) + 2) + 2| - 3)^2 - 3(-1|(1(3sin(2πx + 2) + 3) + 2) + 2| - 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -4(1|(-2(-2sin(3πx - 1) + 3)^2 + 2(-2sin(3πx - 1) + 3) - 1) - 3| - 3)^2 - 3(1|(-2(-2sin(3πx - 1) + 3)^2 + 2(-2sin(3πx - 1) + 3) - 1) - 3| - 3) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 30 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -5(-1sin(2π(3((2x - 2)/(-1x))^2 - 5((2x - 2)/(-1x)) + 5) + 3) - 2) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 70 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 2|(-2sin(2π((3(-3|x + 3| - 3) + 3)/(-2(-3|x + 3| - 3) - 2)) - 1) + 2) - 2| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -2|(-4(-3(-2|x - 2|)^2 - 4(-2|x - 2|)) - 5) + 2| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -1((-1(1|(-1cos(3πx + 1) - 1) + 2| - 3) + 1)/(-2(1|(-1cos(3πx + 1) - 1) + 2| - 3) - 3))^2 - 5((-1(1|(-1cos(3πx + 1) - 1) + 2| - 3) + 1)/(-2(1|(-1cos(3πx + 1) - 1) + 2| - 3) - 3)) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\box... | 143 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -1sin(1π(3|(-5(-1|x - 1| + 3)^2 - 2(-1|x - 1| + 3) + 4) - 3|) - 2) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 255 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (3(2sin(1π((-2(-3|x + 1| + 1) + 3)/(-2(-3|x + 1| + 1) - 1)) + 3) + 3) - 1)/(-3(2sin(1π((-2(-3|x + 1| + 1) + 3)/(-2(-3|x + 1| + 1) - 1)) + 3) + 3) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed... | 34 | MATH |
[
{
"content": "How many local minima does the function f(x) = 2|(-2sin(3π(-1|((2x + 2)/(-2x - 1)) + 1| - 2)) + 3)| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (2((-2(-1sin(2π(5x^2 + 4x - 4) + 2) - 3) - 1)/(-1(-1sin(2π(5x^2 + 4x - 4) + 2) - 3) - 2)) - 3)/(3((-2(-1sin(2π(5x^2 + 4x - 4) + 2) - 3) - 1)/(-1(-1sin(2π(5x^2 + 4x - 4) + 2) - 3) - 2)) + 2) in the interval [-10, 10].\n\nPresent the answer... | 166 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(3(-2|(3cos(1πx + 1) + 3) + 3| - 1) + 1)^2 + 3(3(-2|(3cos(1πx + 1) + 3) + 3| - 1) + 1) + 4 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) = -2sin(3π(1(-1(2x - 5) - 1) + 3) - 3) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1|(-2|(3sin(3π((-1x + 2)/(-2x + 3)) - 3)) - 2| - 2) - 3| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1cos(1π(1(1(2|x|) + 2)^2 - 5(1(2|x|) + 2) - 5) + 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 567 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (1((3(1cos(3π((2x + 1)/(-1x + 2)) - 2)) - 3)/(1(1cos(3π((2x + 1)/(-1x + 2)) - 2)) + 2)) - 3)/(-1((3(1cos(3π((2x + 1)/(-1x + 2)) - 2)) - 3)/(1(1cos(3π((2x + 1)/(-1x + 2)) - 2)) + 2)) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex ... | 75 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(2cos(1π(1((2x)/(-1x + 3))^2 + 2((2x)/(-1x + 3)) + 1) - 3) - 2) - 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 98 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -4(5(-4(-3cos(2πx) - 1) + 2) - 5)^2 + 1(5(-4(-3cos(2πx) - 1) + 2) - 5) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = (-1(-2(-1sin(2π(5x^2 + 5x + 2) + 3) - 3) + 2) + 1)/(3(-2(-1sin(2π(5x^2 + 5x + 2) + 3) - 3) + 2) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 206 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -2(-2sin(2π(-2((-3x - 1)/(1x - 2))^2 - 4((-3x - 1)/(1x - 2)) + 1) + 3) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (-3((3(1|(-1sin(1πx + 3) + 1)| + 1) + 3)/(2(1|(-1sin(1πx + 3) + 1)| + 1) - 3)) + 2)/(-1((3(1|(-1sin(1πx + 3) + 1)| + 1) + 3)/(2(1|(-1sin(1πx + 3) + 1)| + 1) - 3))) in the interval [-10, 10].\n\nPresent the answer in LaTex fo... | 20 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -1(1(-3sin(3π((1x + 1)/(2x - 1)) + 3) + 3)^2 + 2(-3sin(3π((1x + 1)/(2x - 1)) + 3) + 3) - 5)^2 + 5(1(-3sin(3π((1x + 1)/(2x - 1)) + 3) + 3)^2 + 2(-3sin(3π((1x + 1)/(2x - 1)) + 3) + 3) - 5) - 2 in the interval [-10, 10].\n\nPresent the answe... | 18 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 3|(3|(2sin(3π(5x^2 - 4x - 2) + 3) - 2) - 2|) + 3| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 245 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (-1(-3|((-1(-3|x| + 2) - 3)/(-3(-3|x| + 2) - 3)) + 2| + 3) + 1)/(-3(-3|((-1(-3|x| + 2) - 3)/(-3(-3|x| + 2) - 3)) + 2| + 3) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-3(5(3|(2sin(1πx - 1) + 2) - 3| + 2)) + 1)/(3(5(3|(2sin(1πx - 1) + 2) - 3| + 2)) + 1) have in the interval [-10, 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) = 3|(-2(2sin(3π(-1x - 2) + 2) - 1)^2 + 1(2sin(3π(-1x - 2) + 2) - 1) + 5) - 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (3(4(-1e^(-1(3x - 3)) + 1) + 5) - 2)/(2(4(-1e^(-1(3x - 3)) + 1) + 5) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many local minima does the function f(x) = -2|(1sin(2π(-5(-1x^2 - 2)^2 + 5(-1x^2 - 2) - 2))) + 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 139 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(-1|(-3sin(2π((2x - 2)/(1x + 2)) + 2)) - 1| - 2) - 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 98 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -1(-2sin(3π(-1|((1x - 2)/(-3x - 2)) + 2| + 1) + 2) + 2) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 3cos(3π(1|(-3(-3|x| + 2) + 4) - 3| - 3) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 270 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (3((1(-3cos(3π((-3x + 2)/(2x + 3)) + 1) - 3) - 3)/(-1(-3cos(3π((-3x + 2)/(2x + 3)) + 1) - 3) + 2)) - 1)/(1((1(-3cos(3π((-3x + 2)/(2x + 3)) + 1) - 3) - 3)/(-1(-3cos(3π((-3x + 2)/(2x + 3)) + 1) - 3) + 2)) - 3) where -10 ≤ x ≤ 10.\n\nPresent... | 61 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 2(-4((-1(1cos(2πx + 3) + 2) + 3)/(3(1cos(2πx + 3) + 2) + 2)) - 2)^2 - 3(-4((-1(1cos(2πx + 3) + 2) + 3)/(3(1cos(2πx + 3) + 2) + 2)) - 2) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 40 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 2cos(2π(4((1(1x + 1) + 2)/(1(1x + 1)))^2 - 5((1(1x + 1) + 2)/(1(1x + 1))) - 3)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 105 | MATH |
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