messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the count of local minima for the function f(x) = -3|(3(1cos(1π(-1|x + 2|) + 1) - 3)^2 - 1(1cos(1π(-1|x + 2|) + 1) - 3)) - 3| + 1 in the interval [-10, 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) = -3(-2(1|(1cos(2πx - 2) + 3) + 1|) + 4) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -3|(2(2(1x^2 + 5x - 3)^2 - 4(1x^2 + 5x - 3) + 3)^2 - 5) - 2| - 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((2((2(3|x + 3| - 2) - 2)/(2(3|x + 3| - 2) - 1)) + 2)/(2((2(3|x + 3| - 2) - 2)/(2(3|x + 3| - 2) - 1)) - 3))^2 - 3((2((2(3|x + 3| - 2) - 2)/(2(3|x + 3| - 2) - 1)) + 2)/(2((2(3|x + 3| - 2) - 2)/(2(3|x + 3| - 2) - 1)) - 3)... | 5 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -1cos(1π(-3|((-3(1|x - 3| - 3) - 1)/(1(1|x - 3| - 3) - 2)) - 2|) - 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -5((3(-1cos(1π(2x + 2) + 3)) - 1)/(1(-1cos(1π(2x + 2) + 3)) - 2))^2 + 3((3(-1cos(1π(2x + 2) + 3)) - 1)/(1(-1cos(1π(2x + 2) + 3)) - 2)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 80 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 3|(3sin(1π(1|(1|x - 3| + 3)| + 2) - 1) - 3) - 3| - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1|(3(2|(2e^(1x) - 2) - 2| - 3)^2 + 3(2|(2e^(1x) - 2) - 2| - 3) - 4)| + 2 have 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) = 3|(3(-2sin(2π(3x - 4) - 2) - 1)^2 + 5(-2sin(2π(3x - 4) - 2) - 1))| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 480 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2(1|(2(-1x^2 - 5x + 2)^2 + 3(-1x^2 - 5x + 2) - 1) - 2|) + 4 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) = 4(-1(-2(-1|x + 1| + 1)^2 - 2(-1|x + 1| + 1) - 1) - 4)^2 + 1(-1(-2(-1|x + 1| + 1)^2 - 2(-1|x + 1| + 1) - 1) - 4) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 7 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 1|(-5(5(5x^2 + 4x - 5)^2 + 5(5x^2 + 4x - 5) + 1) - 1) + 3| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1(-3cos(1π(4(5x^2 + 1x + 2)^2 + 4(5x^2 + 1x + 2) + 3)) - 1) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 144 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 1cos(1π(-3(1|(-1x^2 - 4x + 1)| + 3)^2 - 3(1|(-1x^2 - 4x + 1)| + 3) + 2)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 172 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -4((-1(-2(1cos(1πx) - 3)^2 - 2(1cos(1πx) - 3) + 5) - 2)/(3(-2(1cos(1πx) - 3)^2 - 2(1cos(1πx) - 3) + 5) + 2)) - 4 have in the interval [-10, 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) = 3(-2(3|(3cos(1πx - 3) - 1) - 2|) + 1) - 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((-1(-2(1sin(3πx - 3) - 3)^2 + 3(1sin(3πx - 3) - 3) - 1))/(-1(-2(1sin(3πx - 3) - 3)^2 + 3(1sin(3πx - 3) - 3) - 1) - 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) = 5(-3(1cos(2π(1x - 1)) + 1) - 2)^2 - 3(-3(1cos(2π(1x - 1)) + 1) - 2) + 4 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(3(-2sin(2π(-1|x - 2| + 1) - 3) + 1) - 4) in the interval [-10, 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) = 1(2|(1((3x)/(-2x))^2 - 5((3x)/(-2x)) + 4) - 3|) + 4 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) = -5(3sin(2π(-3|(1|x - 3| - 1)|) + 1) + 3)^2 + 4(3sin(2π(-3|(1|x - 3| - 1)|) + 1) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 243 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 1(-1sin(1π(4(3|x + 3| + 2)^2 + 4(3|x + 3| + 2) - 1) - 3) - 3)^2 - 3(-1sin(1π(4(3|x + 3| + 2)^2 + 4(3|x + 3| + 2) - 1) - 3) - 3) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 209 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 2(3cos(3π(1((3x - 1)/(-1x - 1))^2 - 4((3x - 1)/(-1x - 1)) + 1) - 3) - 1)^2 - 3(3cos(3π(1((3x - 1)/(-1x - 1))^2 - 4((3x - 1)/(-1x - 1)) + 1) - 3) - 1) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 132 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 5((-1(3(-1sin(1πx - 1) - 1) + 3) + 3)/(-3(3(-1sin(1πx - 1) - 1) + 3) - 3))^2 in the interval [-10, 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) = 1((-1(-3|(2sin(2πx) + 3) - 2| - 2) + 2)/(1(-3|(2sin(2πx) + 3) - 2| - 2))) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1|(2(-3cos(2π(-1x + 1) - 2) - 1)^2 - 1(-3cos(2π(-1x + 1) - 2) - 1) - 2) + 1| - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 159 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 3sin(2π(3(-2|(2x^2 + 3x - 3) + 1|) - 1) - 2) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 483 | MATH |
[
{
"content": "How many local minima does the function f(x) = (-2(-1sin(3π(-2|(5x^2 - 2x) + 2| - 1) - 1) + 3) - 1)/(-2(-1sin(3π(-2|(5x^2 - 2x) + 2| - 1) - 1) + 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 218 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 5(1(4(-1cos(1πx - 2) + 3)^2 - 1(-1cos(1πx - 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) = 1|(1|(3sin(3π(4x + 2) - 2) + 2) + 1|) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 479 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 2cos(3π(-5(-1|(4x - 5) - 1| + 3) + 2) + 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 400 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -5(-1cos(2π(-1(3x^2 - 4x - 1)^2 - 3(3x^2 - 4x - 1) + 4) + 3) - 1)^2 - 4(-1cos(2π(-1(3x^2 - 4x - 1)^2 - 3(3x^2 - 4x - 1) + 4) + 3) - 1) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 135 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (3((1(2|(-1cos(2πx + 2) + 2) + 1| - 2) + 3)/(-2(2|(-1cos(2πx + 2) + 2) + 1| - 2) - 1)))/(1((1(2|(-1cos(2πx + 2) + 2) + 1| - 2) + 3)/(-2(2|(-1cos(2πx + 2) + 2) + 1| - 2) - 1)) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: ... | 39 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1(1cos(2π(5(-1|x + 1|)^2 - 4(-1|x + 1|) + 5) + 2) + 2)^2 - 3(1cos(2π(5(-1|x + 1|)^2 - 4(-1|x + 1|) + 5) + 2) + 2) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 223 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -5(2sin(2π((-3(2x^2 - 1x - 4) - 3)/(-3(2x^2 - 1x - 4) + 1)) + 3))^2 + 2(2sin(2π((-3(2x^2 - 1x - 4) - 3)/(-3(2x^2 - 1x - 4) + 1)) + 3)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 18 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (3(2(1sin(3π(1x^2 + 4x - 5) + 3))^2 + 1(1sin(3π(1x^2 + 4x - 5) + 3)) + 1) + 2)/(3(2(1sin(3π(1x^2 + 4x - 5) + 3))^2 + 1(1sin(3π(1x^2 + 4x - 5) + 3)) + 1) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: ... | 498 | MATH |
[
{
"content": "How many local minima does the function f(x) = -4(-2|(-1|(-3sin(3πx + 1) - 1) - 2| - 1) - 2| + 2)^2 + 3 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) = -3sin(2π((-2(-5(-2|x| + 1)^2 - 2(-2|x| + 1) + 5) - 3)/(-2(-5(-2|x| + 1)^2 - 2(-2|x| + 1) + 5) + 3)) + 3) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 3|(-1sin(2π((-3((-2x - 3)/(-3x - 2)) + 2)/(2((-2x - 3)/(-3x - 2)) + 1)) + 2) + 3) - 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (2(2(-5(-1sin(1πx + 1) + 2)^2 + 4(-1sin(1πx + 1) + 2) - 3)^2 + 4(-5(-1sin(1πx + 1) + 2)^2 + 4(-1sin(1πx + 1) + 2) - 3) - 4) + 3)/(3(2(-5(-1sin(1πx + 1) + 2)^2 + 4(-1sin(1πx + 1) + 2) - 3)^2 + 4(-5(-1sin(1πx + 1) + 2)^2 + 4(-1sin(1πx + 1) + 2) - 3)... | 10 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -2|(3e^(2(4(3x - 4))) + 1)| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many local minima does the function f(x) = -3cos(1π(-3(2((3x - 2)/(2x + 3)) + 2)^2 - 3(2((3x - 2)/(2x + 3)) + 2) + 5) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 117 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 2(-2cos(2π(4(-3x - 2) + 2) - 1) - 2) - 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 minima for the function f(x) = (2(2(-4(4x^2 + 3x - 2)^2 + 1(4x^2 + 3x - 2) + 3)^2 - 2(-4(4x^2 + 3x - 2)^2 + 1(4x^2 + 3x - 2) + 3) + 4) - 1)/(-3(2(-4(4x^2 + 3x - 2)^2 + 1(4x^2 + 3x - 2) + 3)^2 - 2(-4(4x^2 + 3x - 2)^2 + 1(4x^2 + 3x - 2) + 3) + 4) + 2) in the interval [-1... | 31 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 1(-2|(-3sin(2π(1|x + 2| + 1) - 3) - 3)| + 1) + 2 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) = -3(-2sin(2π(-4(1x^2 - 3x - 1) - 4) - 3) + 2)^2 + 2(-2sin(2π(-4(1x^2 - 3x - 1) - 4) - 3) + 2) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 450 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 3(3|(-2cos(1π((1x)/(-2x - 1)) - 3) + 3) + 2| + 3)^2 + 5(3|(-2cos(1π((1x)/(-2x - 1)) - 3) + 3) + 2| + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -3(5((1(-2sin(3πx - 2) + 2) - 1)/(-2(-2sin(3πx - 2) + 2) - 2)) - 3)^2 - 2(5((1(-2sin(3πx - 2) + 2) - 1)/(-2(-2sin(3πx - 2) + 2) - 2)) - 3) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 60 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (-2(1(2cos(2π((-2x + 1)/(2x - 3)) - 1) - 2) + 3) + 1)/(-1(1(2cos(2π((-2x + 1)/(2x - 3)) - 1) - 2) + 3) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 1|(1|((1(3sin(3πx - 1) - 3) + 3)/(-2(3sin(3πx - 1) - 3) - 3))| - 2)| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -5((2(-1|(-3sin(2πx + 3) + 1)| + 1))/(-2(-1|(-3sin(2πx + 3) + 1)| + 1) - 3))^2 - 3((2(-1|(-3sin(2πx + 3) + 1)| + 1))/(-2(-1|(-3sin(2πx + 3) + 1)| + 1) - 3)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{You... | 20 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (-1(-5(-1cos(2π((-1x - 2)/(-3x - 1)) + 2) - 1) - 1) + 1)/(2(-5(-1cos(2π((-1x - 2)/(-3x - 1)) + 2) - 1) - 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -4(5((2(3sin(2πx + 3) + 3) + 3)/(-1(3sin(2πx + 3) + 3) - 1))) + 3 where -10 ≤ x ≤ 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) = (1(-2(-3(-1sin(2πx) - 1) - 4) - 3) - 2)/(3(-2(-3(-1sin(2πx) - 1) - 4) - 3) - 2) 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) = (1(-1cos(1π(-1|(-3x^2 - 5x + 2) + 1| + 2) + 3)) + 1)/(3(-1cos(1π(-1|(-3x^2 - 5x + 2) + 1| + 2) + 3)) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 561 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -2sin(2π(1|(-5(-5x^2 - 2x - 4) + 5) - 1| - 3) - 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 235 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -1sin(1π(-1((-1((1x - 2)/(-2x + 3)) - 3)/(-3((1x - 2)/(-2x + 3)) - 2))^2 + 4((-1((1x - 2)/(-2x + 3)) - 3)/(-3((1x - 2)/(-2x + 3)) - 2))) + 3) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 58 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -3cos(2π(-4(3(2x^2 - 1) - 5)^2 + 2) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 67 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1|(1(2(3cos(3πx) - 1)^2 + 5(3cos(3πx) - 1) + 4) + 2) + 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (-3(-4(-3cos(3π(5x^2 - 3x - 5) - 3) + 3)^2 + 2(-3cos(3π(5x^2 - 3x - 5) - 3) + 3) + 5) - 2)/(1(-4(-3cos(3π(5x^2 - 3x - 5) - 3) + 3)^2 + 2(-3cos(3π(5x^2 - 3x - 5) - 3) + 3) + 5) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex... | 357 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -5(3(1sin(3π(-1x^2 + 5x + 2) - 1) + 3) + 3)^2 - 5(3(1sin(3π(-1x^2 + 5x + 2) - 1) + 3) + 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 528 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 1cos(2π(1(-5(-3|x - 1| - 1)^2 + 2(-3|x - 1| - 1) + 5) + 4) - 1) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 226 | MATH |
[
{
"content": "How many local minima does the function f(x) = 4((-2(2(-1cos(3πx - 3) + 3)^2 - 4(-1cos(3πx - 3) + 3) + 5) - 1)/(1(2(-1cos(3πx - 3) + 3)^2 - 4(-1cos(3πx - 3) + 3) + 5) - 2))^2 - 1((-2(2(-1cos(3πx - 3) + 3)^2 - 4(-1cos(3πx - 3) + 3) + 5) - 1)/(1(2(-1cos(3πx - 3) + 3)^2 - 4(-1cos(3πx - 3) + 3) + 5) -... | 30 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -2(-4(1cos(1π(-1x + 5)) - 2) - 3)^2 - 5(-4(1cos(1π(-1x + 5)) - 2) - 3) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 3sin(2π((-3(3((1x + 2)/(3x + 1))^2 - 1((1x + 2)/(3x + 1)) + 2) - 2)/(1(3((1x + 2)/(3x + 1))^2 - 1((1x + 2)/(3x + 1)) + 2) - 3)) - 1) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 53 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (3(-3cos(2π(2|((2x - 1)/(3x + 3))| + 3) + 3) - 3) + 3)/(2(-3cos(2π(2|((2x - 1)/(3x + 3))| + 3) + 3) - 3) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 66 | MATH |
[
{
"content": "How many local minima does the function f(x) = -2|((3(4(-1sin(2πx + 3) - 2) - 2) - 1)/(2(4(-1sin(2πx + 3) - 2) - 2) + 2))| - 2 have 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(-3cos(1π(5(-2x^2 + 4)^2 + 5(-2x^2 + 4) + 2)) - 2) - 1)/(2(-3cos(1π(5(-2x^2 + 4)^2 + 5(-2x^2 + 4) + 2)) - 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 82 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 2(1(-3sin(2π(2|x|) - 3)) + 2) - 4 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) = 1(2|(-5(2|x + 3| - 1) - 1) - 2| - 3)^2 + 4 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) = 2sin(3π(4(-1((1x + 1)/(2x - 3)) + 5)^2 + 2(-1((1x + 1)/(2x - 3)) + 5)) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 219 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 5(-3(3cos(2π((-3x - 1)/(2x + 2)) + 2) + 1))^2 - 4(-3(3cos(2π((-3x - 1)/(2x + 2)) + 2) + 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 5(-1sin(3π(1((3x)/(-3x - 3)) - 1) + 2))^2 + 2(-1sin(3π(1((3x)/(-3x - 3)) - 1) + 2)) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -2|(-3sin(2π(3(5x^2 - 4x + 1) - 5) - 3) - 3) - 2| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 243 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2|(3sin(2π(-1|(-1|x - 2| - 2) + 3| - 1) - 2)) + 3| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(1e^(-2(-4(-5x^2 + 2x + 2)^2 - 4(-5x^2 + 2x + 2) + 4)) + 3)^2 - 5(1e^(-2(-4(-5x^2 + 2x + 2)^2 - 4(-5x^2 + 2x + 2) + 4)) + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 4 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (3(-2sin(3π(2((2x)/(3x + 1)) - 4) - 1) - 1) - 2)/(-3(-2sin(3π(2((2x)/(3x + 1)) - 4) - 1) - 1) + 4) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 5(-3(-2|(3sin(1πx) - 3) - 2| + 2)^2 + 4(-2|(3sin(1πx) - 3) - 2| + 2) - 5) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -2|(1(3(1x^2 - 5x - 1)^2 + 4(1x^2 - 5x - 1) - 3)^2 + 2(3(1x^2 - 5x - 1)^2 + 4(1x^2 - 5x - 1) - 3) + 5) - 1| + 1 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) = -2(-2cos(3π(5(1x - 1)^2 + 4(1x - 1) + 5)) + 1) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 248 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1(3sin(3π(4((3x - 2)/(-2x + 3))^2 + 2((3x - 2)/(-2x + 3)) - 4) + 1) - 1) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 103 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -3(-3cos(1π(1(-3|x - 3| + 1) - 1) - 3) + 1)^2 - 1(-3cos(1π(1(-3|x - 3| + 1) - 1) - 3) + 1) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -1(1(-3sin(3π((-3x + 1)/(-1x - 2)) - 3) - 1) - 4)^2 + 1(1(-3sin(3π((-3x + 1)/(-1x - 2)) - 3) - 1) - 4) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(2sin(1π(-5(2|x + 3| - 1))) - 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 201 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -1|(-1(-1(2|x + 1| + 2) + 2)^2 - 2(-1(2|x + 1| + 2) + 2) + 5) + 1| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "How many local minima does the function f(x) = 2cos(1π(2|(-1(3|x + 1| + 2)^2 - 4(3|x + 1| + 2) + 4) + 1| + 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 259 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -5(-1(3sin(1π(-2|x + 1| + 1) + 1) + 2)^2 - 2(3sin(1π(-2|x + 1| + 1) + 1) + 2) + 5)^2 + 5(-1(3sin(1π(-2|x + 1| + 1) + 1) + 2)^2 - 2(3sin(1π(-2|x + 1| + 1) + 1) + 2) + 5) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 40 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -4(-3sin(2π(-4(4x - 4) - 5) - 1) + 3) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 640 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1|(3cos(2π(3(5x - 5)^2 - 5(5x - 5) - 1)) - 3) - 3| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 404 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 4(2(5(1cos(3πx - 3) - 1)^2 + 5(1cos(3πx - 3) - 1) - 5)^2 + 3(5(1cos(3πx - 3) - 1)^2 + 5(1cos(3πx - 3) - 1) - 5)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 180 | MATH |
[
{
"content": "How many local minima does the function f(x) = (-1(-2|((-1(1sin(3πx + 3) - 1) + 1)/(1(1sin(3πx + 3) - 1) + 3)) + 2|) + 1)/(-1(-2|((-1(1sin(3πx + 3) - 1) + 1)/(1(1sin(3πx + 3) - 1) + 3)) + 2|) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 30 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 2|(5(-2sin(1π((1x - 2)/(-2x + 3)) - 1) - 2) + 2) - 2| 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|(-5((-1(3sin(3πx) - 2) + 3)/(-3(3sin(3πx) - 2) - 1)) - 4) + 3| + 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 maxima does the function f(x) = (-1(-2sin(2π(-5(3|x + 1| - 3)^2 + 5(3|x + 1| - 3) - 3) - 2) - 1) - 1)/(3(-2sin(2π(-5(3|x + 1| - 3)^2 + 5(3|x + 1| - 3) - 3) - 2) - 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 163 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -4(-1|((1(2cos(2πx - 1) + 3) - 1)/(-2(2cos(2πx - 1) + 3) - 2)) + 1| + 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) = (-1(-2cos(3π(3(-3|x + 1| - 3)^2 - 2(-3|x + 1| - 3)) - 1) - 1) + 2)/(3(-2cos(3π(3(-3|x + 1| - 3)^2 - 2(-3|x + 1| - 3)) - 1) - 1) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 221 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -3|(2cos(2π(3(-1|x - 1| + 1) + 2) - 1) + 3) + 1| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(2sin(3π((-1(-2|x + 3|) - 2)/(-2(-2|x + 3|) - 1)) - 3))^2 + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -2|(-3cos(2π((2(2x + 1) - 2)/(2(2x + 1) + 1)) + 2) - 3) - 3| - 2 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 maxima for the function f(x) = -3cos(3π(-5(3|(1|x - 2|) + 2|)^2 - 5(3|(1|x - 2|) + 2|) - 1) - 2) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 183 | MATH |
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