messages listlengths 1 1 | ground_truth stringclasses 194
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "How many local minima does the function f(x) = 2((-1x + 2)/(-2x - 3))^2 - 3((-1x + 2)/(-2x - 3)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 2sin(2π(-5x - 1) - 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -2(-3|(4x - 4)| + 1)^2 + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = (-3(-1sin(3π(1(-2|x - 2| + 2) + 3) + 2) + 2) + 3)/(-2(-1sin(3π(1(-2|x - 2| + 2) + 3) + 2) + 2) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1cos(2π(1|((3(-4x) + 1)/(-1(-4x) + 3)) + 1| - 3) - 1) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 1sin(3π(5x^2 - 5x + 1) - 3) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 253 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 2e^(-1(3|(4(1x^2 - 4x + 1)) + 3| + 1)) - 3 in the interval [-10, 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) = -2(4(2sin(3π(2|x - 2| - 3) + 1))^2 + 4(2sin(3π(2|x - 2| - 3) + 1)) + 1) + 3 in the interval [-10, 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) = 3sin(1π((1(-1(-1|x + 2| + 2) - 4) + 2)/(-1(-1(-1|x + 2| + 2) - 4) + 2)) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 2|(-3e^(1(-4((-3x)/(-1x + 3))^2 + 4((-3x)/(-1x + 3)) + 2)))| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1e^(-1(1(-3|x + 3| + 3)^2 - 4)) + 2 have 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) = -3sin(3π(-3(-2|((2x - 3)/(3x + 2)) + 3| - 1)^2 + 4(-2|((2x - 3)/(3x + 2)) + 3| - 1)) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 184 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -3cos(1π(-1|(4x^2 + 4x + 3) - 3| + 1) + 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 291 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -1(-1sin(2π(-3|(1x^2 - 2x - 2) - 3| - 3) - 3)) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 465 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 2(2|(-2sin(1πx - 2) - 1)| + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 4(2|(4x^2 + 3x - 5) + 3|) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1|(4(-1((3x + 1)/(-2x)))^2 + 4(-1((3x + 1)/(-2x))) - 4) + 1| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-1(1sin(1πx + 1) - 2))/(-1(1sin(1πx + 1) - 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 5((-3(2|(1e^(-1x) - 2)| - 3))/(1(2|(1e^(-1x) - 2)| - 3) + 2))^2 - 5((-3(2|(1e^(-1x) - 2)| - 3))/(1(2|(1e^(-1x) - 2)| - 3) + 2)) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (1(-3(2(-1cos(1πx + 2) - 1)^2 + 4(-1cos(1πx + 2) - 1) + 1) + 4) - 3)/(-2(-3(2(-1cos(1πx + 2) - 1)^2 + 4(-1cos(1πx + 2) - 1) + 1) + 4) + 1) 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((-1(-2cos(1πx - 1) + 2) - 3)/(-1(-2cos(1πx - 1) + 2) - 2)) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (-3(-1(-2|(3x - 3) - 3| + 2)^2 - 3(-2|(3x - 3) - 3| + 2) + 3) + 1)/(2(-1(-2|(3x - 3) - 3| + 2)^2 - 3(-2|(3x - 3) - 3| + 2) + 3) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 2 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 1(2cos(3πx - 1) + 3)^2 + 2(2cos(3πx - 1) + 3) - 4 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) = 1sin(2π(5x^2 - 4x) - 3) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 251 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -3cos(2π(2x^2 - 2x + 2) + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 284 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 2sin(3π(-2|(1x^2 + 5x - 4) - 2|) - 1) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 515 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (3(1(2sin(1π(-1|x - 3| + 1) + 2))^2 - 2(2sin(1π(-1|x - 3| + 1) + 2)) + 3) + 1)/(-1(1(2sin(1π(-1|x - 3| + 1) + 2))^2 - 2(2sin(1π(-1|x - 3| + 1) + 2)) + 3) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your ... | 29 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -5(-1cos(1πx - 3) - 1)^2 + 3(-1cos(1πx - 3) - 1) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 1sin(2π(1(2|x + 2| + 1)^2 + 4(2|x + 2| + 1) + 1) + 2) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 265 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -4((-1(2sin(1π(4x + 3) - 2) + 2) + 2)/(-1(2sin(1π(4x + 3) - 2) + 2)))^2 + 2((-1(2sin(1π(4x + 3) - 2) + 2) + 2)/(-1(2sin(1π(4x + 3) - 2) + 2))) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 160 | MATH |
[
{
"content": "How many local minima does the function f(x) = 5(-5(3e^(-2(2|x|)) + 1)^2 - 2(3e^(-2(2|x|)) + 1) + 3) + 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 maxima does the function f(x) = 3(-1sin(2πx - 1) + 3)^2 + 5(-1sin(2πx - 1) + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2cos(2π(5x) - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -5(-1|x| + 2)^2 + 5(-1|x| + 2) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 2|(1sin(1πx) - 1) + 3| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -3|((-1(3e^(-2(5x + 2)) - 1) - 3)/(1(3e^(-2(5x + 2)) - 1) - 3)) - 2| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 3|(-1cos(1π(-2x - 4) - 1) + 2) - 1| - 1 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) = -4(2sin(2π((-1x - 1)/(1x + 2)) + 1) + 1)^2 + 3(2sin(2π((-1x - 1)/(1x + 2)) + 1) + 1) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -3((-1(-2|(1cos(2πx - 2) - 2) - 1| + 1))/(-2(-2|(1cos(2πx - 2) - 2) - 1| + 1) + 1)) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -2((2x - 3)/(3x - 1))^2 - 5((2x - 3)/(3x - 1)) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 3(-2sin(1π(-2|x - 1|) - 2) - 2) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -1(-2|((1(3x + 2) - 2)/(-2(3x + 2) - 1)) - 3| + 3)^2 - 5(-2|((1(3x + 2) - 2)/(-2(3x + 2) - 1)) - 3| + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 3((-1(-1|(-4x^2 - 1x + 2) + 2| - 2) - 1)/(-2(-1|(-4x^2 - 1x + 2) + 2| - 2))) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4(3cos(2π(-4x + 5) - 3) + 3)^2 - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (-2(-3sin(2πx - 2) + 2) + 2)/(-2(-3sin(2πx - 2) + 2) - 1) 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) = 2((2(-2(-2|x| + 3)^2 - 1(-2|x| + 3) - 2) + 2)/(-3(-2(-2|x| + 3)^2 - 1(-2|x| + 3) - 2) + 4)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 2sin(3π((1(1(-3|x - 3| + 3) - 3) + 3)/(2(1(-3|x - 3| + 3) - 3))) - 1) - 3 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|(-2sin(2π(1(2x^2 + 1x - 3) - 2) - 3) - 1) - 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 286 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -2|(5(2sin(2π(-3x^2 + 1x - 3) + 2) - 2) - 4) + 2| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 449 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (-3(-4(3|x + 1|) + 4))/(-2(-4(3|x + 1|) + 4)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (-1(3sin(2πx - 2) - 2) + 1)/(-1(3sin(2πx - 2) - 2) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -3(1|(-5(2sin(3πx - 1) + 1)^2 + 2)| + 3) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 238 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (-2(-1cos(3πx + 3) + 2) - 3)/(-2(-1cos(3πx + 3) + 2) + 3) where -10 ≤ x ≤ 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) = 2e^(-1(3(-1|((3x - 3)/(2x - 3)) - 3| + 3)^2 + 1(-1|((3x - 3)/(2x - 3)) - 3| + 3) + 4)) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -3|(-1x^2 - 5x + 2) - 1| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -2e^(-1(-4x + 1)) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -1cos(2π((3x - 2)/(3x + 3)) + 2) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 2cos(3π(1|((-1x + 1)/(1x + 2)) + 3| - 3) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -3|(-3((3x - 2)/(2x + 1))^2 + 1((3x - 2)/(2x + 1)) + 1) + 1| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-4(-2|((-2x)/(3x)) - 2| + 2) - 2)^2 - 4(-4(-2|((-2x)/(3x)) - 2| + 2) - 2) - 4 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(-2sin(3πx + 2) - 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (3(2sin(1π(3|(5x^2 + 2x + 2) - 3| - 2) - 2) + 1) - 2)/(-2(2sin(1π(3|(5x^2 + 2x + 2) - 3| - 2) - 2) + 1) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 501 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1sin(3π(-3|(1(-5x^2 - 1x + 4) + 1) + 3| - 2) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 245 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -4(1cos(2π(-3|(1x^2 - 1x - 1) + 2| - 3) - 3)) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 230 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 3sin(1π(-4(4x^2 + 4x) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 238 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -3((-1(3cos(3πx - 1) + 3) - 2)/(-1(3cos(3πx - 1) + 3) + 2))^2 + 1((-1(3cos(3πx - 1) + 3) - 2)/(-1(3cos(3πx - 1) + 3) + 2)) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 119 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 1|(-1cos(2π(2x^2 + 3x + 2) - 2) - 2) + 1| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 289 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -1(5(2|(1sin(1πx) + 2) - 1| + 2)^2 + 4(2|(1sin(1πx) + 2) - 1| + 2) - 3) + 5 where -10 ≤ x ≤ 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) = -3((-2(-2cos(3πx + 3) + 1))/(2(-2cos(3πx + 3) + 1) - 1)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -1sin(2π(2(3|x + 3| - 3) - 5)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 241 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 4(2((1x + 3)/(3x + 3)) + 5)^2 - 3(2((1x + 3)/(3x + 3)) + 5) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many local minima does the function f(x) = -2e^(-1(3((1(-3|x - 3| + 3) - 2)/(1(-3|x - 3| + 3)))^2 + 4((1(-3|x - 3| + 3) - 2)/(1(-3|x - 3| + 3))) + 5)) - 3 have 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) = 1sin(2π((-2(4x^2 + 1x) - 3)/(-2(4x^2 + 1x))) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -2|(2cos(1πx - 1) - 1) + 2| + 1 in the interval [-10, 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(-3cos(3πx - 3) + 3) - 1 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 maximum points for f(x) = 1|(1sin(2π((-3(2x^2 + 4x + 3) + 3)/(-1(2x^2 + 4x + 3) - 3))) + 2) + 2| - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1sin(3π((-3(-3x - 2) - 2)/(1(-3x - 2) + 3)) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 2sin(2π(-2|x - 1| + 1)) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 2((-3(2|x - 3| - 3))/(1(2|x - 3| - 3))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -1(5((-3(-1|x - 1| - 2))/(1(-1|x - 1| - 2))))^2 - 1(5((-3(-1|x - 1| - 2))/(1(-1|x - 1| - 2)))) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 133 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (-2(1(-1|(-2cos(1πx - 2) + 3)| - 3) - 2))/(2(1(-1|(-2cos(1πx - 2) + 3)| - 3) - 2) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 4(3((2x - 1)/(-3x - 1)) + 5)^2 + 5(3((2x - 1)/(-3x - 1)) + 5) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 3|(-1cos(3πx - 3) - 2) + 3| - 1 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 minima for the function f(x) = -1(-1sin(2π(-1|x - 3| + 1) + 2) - 3)^2 + 1(-1sin(2π(-1|x - 3| + 1) + 2) - 3) + 3 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 maximum points for f(x) = (3(-3|(1cos(1π(4x - 3) - 2) + 1) - 2| + 1) - 3)/(2(-3|(1cos(1π(4x - 3) - 2) + 1) - 2| + 1) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 3|(-5((3x + 1)/(-2x + 3))^2 + 3)| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 2(1|(1((-1x + 2)/(-3x - 3)) - 4)| - 1)^2 + 2(1|(1((-1x + 2)/(-3x - 3)) - 4)| - 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|(-5(-2cos(3πx - 2) + 1)^2 - 2(-2cos(3πx - 2) + 1)) - 3| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 5(3sin(2π(1((1x - 2)/(1x + 2)) - 4)) - 3)^2 + 5(3sin(2π(1((1x - 2)/(1x + 2)) - 4)) - 3) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 3|(-1cos(1π(4x^2 - 1) - 2) + 1) + 2| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 292 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -3e^(-2(-3x^2 - 2x + 1)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (2(1|(-2sin(2π(5x - 3) + 3)) + 3| - 1) + 2)/(2(1|(-2sin(2π(5x - 3) + 3)) + 3| - 1) + 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) = -1(-2cos(3πx - 2) - 3) + 2 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) = 3e^(1(-2x^2 - 1x)) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -5(-1|(-2cos(1πx - 2) - 3) - 3| - 3) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 2(1cos(3πx + 1) - 1) + 4 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) = 1(-1sin(3πx - 2) + 2) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1|(2sin(3πx - 1) - 1) - 3| + 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) = 2|(-1sin(3π((-3(1x) - 3)/(1(1x))) + 1) - 3) - 2| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 1(-2cos(2π(4x^2 + 3) - 1) - 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 261 | MATH |
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