messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "How many local minima does the function f(x) = -2(1|((-3(1sin(2π(3(-4x + 5) - 4) - 3) - 3) - 2)/(-2(1sin(2π(3(-4x + 5) - 4) - 3) - 3) + 1)) + 3| + 1)^2 + 5(1|((-3(1sin(2π(3(-4x + 5) - 4) - 3) - 3) - 2)/(-2(1sin(2π(3(-4x + 5) - 4) - 3) - 3) + 1)) + 3| + 1) + 3 have in the interval [-10, 10]?\n\nPre... | 240 | MATH |
[
{
"content": "How many local minima does the function f(x) = -3(3|(-5(-2sin(1π(-2(-3x^2 - 1x + 2) - 4) + 2) + 1) - 4) - 3| - 2)^2 + 1(3|(-5(-2sin(1π(-2(-3x^2 - 1x + 2) - 4) + 2) + 1) - 4) - 3| - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 168 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 5(4((-2(-2sin(2π(-3|(-3x^2 - 4x + 4) - 2| + 3) - 3) + 1) + 1)/(1(-2sin(2π(-3|(-3x^2 - 4x + 4) - 2| + 3) - 3) + 1) - 3))^2 - 4((-2(-2sin(2π(-3|(-3x^2 - 4x + 4) - 2| + 3) - 3) + 1) + 1)/(1(-2sin(2π(-3|(-3x^2 - 4x + 4) - 2| + 3) - 3) + 1) - ... | 151 | MATH |
[
{
"content": "How many local minima does the function f(x) = -2((1(-5(2(5(1x^2 - 3x + 5) - 1)^2 - 4)^2 + 2(2(5(1x^2 - 3x + 5) - 1)^2 - 4) + 4) - 3)/(-3(-5(2(5(1x^2 - 3x + 5) - 1)^2 - 4)^2 + 2(2(5(1x^2 - 3x + 5) - 1)^2 - 4) + 4) + 1)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\b... | 5 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -3(-3|((-3(-1(-1(-2cos(3πx + 2) + 3)^2 + 3(-2cos(3πx + 2) + 3) + 2) - 5) + 2)/(1(-1(-1(-2cos(3πx + 2) + 3)^2 + 3(-2cos(3πx + 2) + 3) + 2) - 5) - 3)) + 1| + 3)^2 + 5(-3|((-3(-1(-1(-2cos(3πx + 2) + 3)^2 + 3(-2cos(3πx + 2) + 3)... | 252 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -4(-2(3((2(-1(-2sin(2πx + 1) - 2) - 5))/(-3(-1(-2sin(2πx + 1) - 2) - 5) + 1))^2 + 5((2(-1(-2sin(2πx + 1) - 2) - 5))/(-3(-1(-2sin(2πx + 1) - 2) - 5) + 1)) + 5)^2 + 1)^2 + 5(-2(3((2(-1(-2sin(2πx + 1) - 2) - 5))/(-3(-1(-2sin(2πx + 1) - 2) - 5) + 1))^... | 20 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 5(-1|(3|(1sin(2π((1((3x - 3)/(-1x + 3)) + 3)/(2((3x - 3)/(-1x + 3)) + 3)) - 2) + 2)|) - 3| - 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (-2(2cos(2π((-1(-3(-4(-1|x + 1| + 1) - 3) - 2) + 2)/(-2(-3(-4(-1|x + 1| + 1) - 3) - 2) - 3)) + 1)) - 2)/(3(2cos(2π((-1(-3(-4(-1|x + 1| + 1) - 3) - 2) + 2)/(-2(-3(-4(-1|x + 1| + 1) - 3) - 2) - 3)) + 1))) in the interval [-10, 10].\n\nPrese... | 14 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (-1(1(-2cos(2π(1(-3(-2|x - 3|)^2 - 5(-2|x - 3|) - 1)) - 1) - 1)^2 - 1(-2cos(2π(1(-3(-2|x - 3|)^2 - 5(-2|x - 3|) - 1)) - 1) - 1) + 1) + 3)/(-3(1(-2cos(2π(1(-3(-2|x - 3|)^2 - 5(-2|x - 3|) - 1)) - 1) - 1)^2 - 1(-2cos(2π(1(-3(-2... | 461 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (2(-2cos(3π(-1((-2((1(-2x - 5) - 2)/(-2(-2x - 5) - 2)) + 1)/(-2((1(-2x - 5) - 2)/(-2(-2x - 5) - 2))))) + 1) + 2) - 3)/(3(-2cos(3π(-1((-2((1(-2x - 5) - 2)/(-2(-2x - 5) - 2)) + 1)/(-2((1(-2x - 5) - 2)/(-2(-2x - 5) - 2))))) + 1) + 2) + 3) wh... | 42 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (-2((3(-1(-4((-1(1cos(2πx + 2)) - 1)/(-1(1cos(2πx + 2)) - 2)) - 2) + 3) + 2)/(-2(-1(-4((-1(1cos(2πx + 2)) - 1)/(-1(1cos(2πx + 2)) - 2)) - 2) + 3) - 2)) + 2)/(1((3(-1(-4((-1(1cos(2πx + 2)) - 1)/(-1(1cos(2πx + 2)) - 2)) - 2) + 3) + 2)/(-2(-... | 20 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -3|(4((2((2(2(-3|x + 1| + 3)^2 - 4(-3|x + 1| + 3) - 4) - 3)/(1(2(-3|x + 1| + 3)^2 - 4(-3|x + 1| + 3) - 4) + 2)) - 3)/(-2((2(2(-3|x + 1| + 3)^2 - 4(-3|x + 1| + 3) - 4) - 3)/(1(2(-3|x + 1| + 3)^2 - 4(-3|x + 1| + 3) - 4) + 2)) - 2)) - 1) + 2| - 3 whe... | 5 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (-2(-4(-1((3(-5(-1e^(2x) + 1)^2 + 4(-1e^(2x) + 1) - 4) - 2)/(2(-5(-1e^(2x) + 1)^2 + 4(-1e^(2x) + 1) - 4) - 1)) + 5)^2 - 3(-1((3(-5(-1e^(2x) + 1)^2 + 4(-1e^(2x) + 1) - 4) - 2)/(2(-5(-1e^(2x) + 1)^2 + 4(-1e^(2x) + 1) - 4) - 1)) + 5) - 2) + ... | 27 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (1((1(2(2e^(2(-1(-3|x + 2| + 3) + 4)) - 1) - 4) + 2)/(1(2(2e^(2(-1(-3|x + 2| + 3) + 4)) - 1) - 4) + 1)))/(-2((1(2(2e^(2(-1(-3|x + 2| + 3) + 4)) - 1) - 4) + 2)/(1(2(2e^(2(-1(-3|x + 2| + 3) + 4)) - 1) - 4) + 1)) + 1) where -10 ≤ x ≤ 10.\n\n... | 10 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2|(-4(2|((-3(-1|(-2x^2 + 5x + 5) + 2| + 2))/(-3(-1|(-2x^2 + 5x + 5) + 2| + 2) + 4)) - 2| + 3) + 2) - 2| - 1 have in the interval [-10, 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) = 4(5(3|((-2(4((-2x - 2)/(1x))^2 + 5((-2x - 2)/(1x)) - 3) - 2)/(-3(4((-2x - 2)/(1x))^2 + 5((-2x - 2)/(1x)) - 3) + 1))| + 1)^2 - 2(3|((-2(4((-2x - 2)/(1x))^2 + 5((-2x - 2)/(1x)) - 3) - 2)/(-3(4((-2x - 2)/(1x))^2 + 5((-2x - 2)/(1x)) - 3) + 1)... | 5 | MATH |
[
{
"content": "How many local minima does the function f(x) = (3(5(-3(3(-1|(1x + 2) - 2| + 2)^2 + 1(-1|(1x + 2) - 2| + 2) + 4) + 1) - 4))/(1(5(-3(3(-1|(1x + 2) - 2| + 2)^2 + 1(-1|(1x + 2) - 2| + 2) + 4) + 1) - 4)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 74 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1sin(1π(2(-4(1|((-3(-3|x + 2| - 1) - 2)/(2(-3|x + 2| - 1))) + 3| + 2) + 2)^2 + 3)) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 138 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (-1((-3(-3(-4(-3cos(1π(2|x| - 3) - 3))) + 3) + 1)/(1(-3(-4(-3cos(1π(2|x| - 3) - 3))) + 3) + 1)) + 2)/(-3((-3(-3(-4(-3cos(1π(2|x| - 3) - 3))) + 3) + 1)/(1(-3(-4(-3cos(1π(2|x| - 3) - 3))) + 3) + 1))) in the interval [-10, 10].\n\nPresent th... | 20 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1(2|(2e^(-2((1(-1((2x + 3)/(-1x - 1))^2 - 3((2x + 3)/(-1x - 1)) - 3) + 2)/(-2(-1((2x + 3)/(-1x - 1))^2 - 3((2x + 3)/(-1x - 1)) - 3) - 2))) - 3) - 1| - 2)^2 + 1(2|(2e^(-2((1(-1((2x + 3)/(-1x - 1))^2 - 3((2x + 3)/(-1x - 1)) - 3) + 2)/(-2(-1((2x + 3)/(-1... | 8 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2((-1(-2|(-1|(-5(4x - 5) - 2) + 2| + 3) - 3| - 1) - 1)/(-3(-2|(-1|(-5(4x - 5) - 2) + 2| + 3) - 3| - 1) - 3)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 222 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 2|(1|((2(-1(-2cos(1π(-1x^2 - 1x + 2) - 1) + 3) - 4) + 3)/(3(-1(-2cos(1π(-1x^2 - 1x + 2) - 1) + 3) - 4) - 2)) - 1| + 1) - 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 101 | MATH |
[
{
"content": "How many local minima does the function f(x) = -2cos(2π(3|(2(3|((3(2|x - 3| + 1) - 3)/(-1(2|x - 3| + 1) - 3)) + 2| - 1)^2 + 3(3|((3(2|x - 3| + 1) - 3)/(-1(2|x - 3| + 1) - 3)) + 2| - 1) - 3)| - 3) - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 99 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (-3(4((-2(2|((-3(-3sin(2πx - 2) - 1) - 3)/(-2(-3sin(2πx - 2) - 1))) - 3| + 1) - 3)/(3(2|((-3(-3sin(2πx - 2) - 1) - 3)/(-2(-3sin(2πx - 2) - 1))) - 3| + 1))) + 3) + 2)/(1(4((-2(2|((-3(-3sin(2πx - 2) - 1) - 3)/(-2(-3sin(2πx - 2... | 117 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 1(3cos(3π(3(-4(-4(-2|x - 2| + 2)^2 + 3(-2|x - 2| + 2)) + 3) + 3) + 1) - 3)^2 + 2(3cos(3π(3(-4(-4(-2|x - 2| + 2)^2 + 3(-2|x - 2| + 2)) + 3) + 3) + 1) - 3) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 133 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -1|(-2(1sin(1π(3(-5(-3|x - 3| - 2)^2 - 1)^2 + 1(-5(-3|x - 3| - 2)^2 - 1) + 3) + 3) + 2) - 1) - 3| + 3 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 minima for the function f(x) = -1(-3(-3|(-1((2((2x)/(1x - 2)) - 1)/(3((2x)/(1x - 2)) + 1))^2 - 4((2((2x)/(1x - 2)) - 1)/(3((2x)/(1x - 2)) + 1)) + 1)| + 1)^2 + 3(-3|(-1((2((2x)/(1x - 2)) - 1)/(3((2x)/(1x - 2)) + 1))^2 - 4((2((2x)/(1x - 2)) - 1)/(3((2x)/(1x - 2)) + 1)) +... | 5 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 2(-4(2(1|(-1(1sin(1πx - 1) + 3)^2 + 2(1sin(1πx - 1) + 3) - 2) + 1| + 2) - 2)^2 - 3(2(1|(-1(1sin(1πx - 1) + 3)^2 + 2(1sin(1πx - 1) + 3) - 2) + 1| + 2) - 2) - 4)^2 - 3(-4(2(1|(-1(1sin(1πx - 1) + 3)^2 + 2(1sin(1πx - 1) + 3) - 2... | 12 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (-1(5(3sin(1π(3((-1(-1|x + 2| - 2) + 2)/(-2(-1|x + 2| - 2) - 1)) - 1) - 1) - 2) + 3) - 2)/(2(5(3sin(1π(3((-1(-1|x + 2| - 2) + 2)/(-2(-1|x + 2| - 2) - 1)) - 1) - 1) - 2) + 3) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex f... | 4 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -1|(-1(-4(2sin(2π(-3|(4x) + 3| - 1) + 1) - 3)^2 + 1(2sin(2π(-3|(4x) + 3| - 1) + 1) - 3) - 3)^2 + 1) + 3| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 477 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(3|(1cos(2π((1(4(3x - 1) + 5) - 3)/(-2(4(3x - 1) + 5) - 3)) + 1) - 1) + 2| - 2) + 1)/(-2(3|(1cos(2π((1(4(3x - 1) + 5) - 3)/(-2(4(3x - 1) + 5) - 3)) + 1) - 1) + 2| - 2) - 3) have in the interval [-10, 10]?\n\nPresent the... | 14 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (-2(5(1cos(2π(-2(4(-1x + 5) + 4) - 5) - 2) + 1)^2 + 4(1cos(2π(-2(4(-1x + 5) + 4) - 5) - 2) + 1) + 1) + 3)/(2(5(1cos(2π(-2(4(-1x + 5) + 4) - 5) - 2) + 1)^2 + 4(1cos(2π(-2(4(-1x + 5) + 4) - 5) - 2) + 1) + 1) - 1) in the interv... | 320 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-3(2|(3((2(2(-1x^2 - 4x)^2 + 5(-1x^2 - 4x) - 1))/(-2(2(-1x^2 - 4x)^2 + 5(-1x^2 - 4x) - 1) - 2))^2 - 1((2(2(-1x^2 - 4x)^2 + 5(-1x^2 - 4x) - 1))/(-2(2(-1x^2 - 4x)^2 + 5(-1x^2 - 4x) - 1) - 2)) + 3) + 1| - 2) + 1)/(2(2|(3((2... | 11 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (-1(-2sin(2π(-2(-1|(5(1|x - 2| - 3) - 1) - 1| - 2)^2 - 3(-1|(5(1|x - 2| - 3) - 1) - 1| - 2) + 2) + 2) + 1))/(2(-2sin(2π(-2(-1|(5(1|x - 2| - 3) - 1) - 1| - 2)^2 - 3(-1|(5(1|x - 2| - 3) - 1) - 1| - 2) + 2) + 2) + 1) + 1) in the interval [-1... | 335 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -2|((-2(-2sin(3π((-3(4(3x^2 - 4) - 4) + 3)/(1(4(3x^2 - 4) - 4) + 1)) + 1) - 2) - 1)/(3(-2sin(3π((-3(4(3x^2 - 4) - 4) + 3)/(1(4(3x^2 - 4) - 4) + 1)) + 1) - 2) + 1)) - 2| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format:... | 8 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = (1(-1(-2|((-1(3|(1sin(3πx + 3) + 2) + 1| - 2) - 2)/(2(3|(1sin(3πx + 3) + 2) + 1| - 2) + 1))| - 1)^2 - 5(-2|((-1(3|(1sin(3πx + 3) + 2) + 1| - 2) - 2)/(2(3|(1sin(3πx + 3) + 2) + 1| - 2) + 1))| - 1) + 3) + 2)/(-2(-1(-2|((-1(3|(1sin(3πx + 3) + 2) + 1|... | 30 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -2|(3((3(1sin(3π(3(3x - 1)^2 - 1(3x - 1) - 5) + 2)) - 2)/(-3(1sin(3π(3(3x - 1)^2 - 1(3x - 1) - 5) + 2)) - 3)) - 3) + 2| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (-2((1(-3|(-1(-2sin(3π(1|x + 3| - 2) + 1)) - 5) - 2| - 1) + 1)/(2(-3|(-1(-2sin(3π(1|x + 3| - 2) + 1)) - 5) - 2| - 1) - 3)) + 3)/(-1((1(-3|(-1(-2sin(3π(1|x + 3| - 2) + 1)) - 5) - 2| - 1) + 1)/(2(-3|(-1(-2sin(3π(1|x + 3| - 2) ... | 61 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3|((-3(4(2|(2cos(1π(2|x + 1| + 3) - 1) + 1) + 2| + 2)^2 + 5(2|(2cos(1π(2|x + 1| + 3) - 1) + 1) + 2| + 2) + 1) + 3)/(1(4(2|(2cos(1π(2|x + 1| + 3) - 1) + 1) + 2| + 2)^2 + 5(2|(2cos(1π(2|x + 1| + 3) - 1) + 1) + 2| + 2) + 1))... | 41 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -2|((1(2sin(3π(1(-1(1x - 5) + 1) - 4) - 2) + 1) - 2)/(2(2sin(3π(1(-1(1x - 5) + 1) - 4) - 2) + 1))) + 2| - 1 where -10 ≤ x ≤ 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) = -4(3|(2((3(1cos(3π(4x - 2) - 2) + 2) + 1)/(-3(1cos(3π(4x - 2) - 2) + 2) + 2))^2 - 2((3(1cos(3π(4x - 2) - 2) + 2) + 1)/(-3(1cos(3π(4x - 2) - 2) + 2) + 2)) + 2) + 1| + 3)^2 + 1(3|(2((3(1cos(3π(4x - 2) - 2) + 2) + 1)/(-3(1cos(3π(4x - 2) - 2) + 2) + 2))^2... | 59 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -2(-3|(5(-3(-2e^(1(1x + 2)) + 2)^2 - 3(-2e^(1(1x + 2)) + 2) + 5)^2 + 1(-3(-2e^(1(1x + 2)) + 2)^2 - 3(-2e^(1(1x + 2)) + 2) + 5) + 1) - 2| + 1) + 2 where -10 ≤ x ≤ 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((-2(-2|(-1(4((2x)/(-2x - 3))^2 - 5((2x)/(-2x - 3)) - 2)^2 - 5(4((2x)/(-2x - 3))^2 - 5((2x)/(-2x - 3)) - 2) - 1) - 1| - 1) + 3)/(2(-2|(-1(4((2x)/(-2x - 3))^2 - 5((2x)/(-2x - 3)) - 2)^2 - 5(4((2x)/(-2x - 3))^2 - 5((2x)/(-2x - 3)) - 2) - 1... | 6 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -2cos(3π(-2|((-2(-1(-5(2|x - 2| - 2)^2 + 1(2|x - 2| - 2) + 5) - 2) + 2)/(-3(-1(-5(2|x - 2| - 2)^2 + 1(2|x - 2| - 2) + 5) - 2) - 3))| - 3) - 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 21 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -2|((3(-1(3(-1sin(1π(3|x - 3| + 2) + 1) + 1)^2 - 2(-1sin(1π(3|x - 3| + 2) + 1) + 1) + 1)^2 + 5(3(-1sin(1π(3|x - 3| + 2) + 1) + 1)^2 - 2(-1sin(1π(3|x - 3| + 2) + 1) + 1) + 1) - 5) + 3)/(-2(-1(3(-1sin(1π(3|x - 3| + 2) + 1) + 1)^2 - 2(-1sin(... | 268 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -5(-1(-1cos(1π(-1(1|(-5x - 3) - 1| + 1) - 3) + 2) + 3) - 4) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3|(3(2cos(1π(-4((-1(3x^2 - 5) - 1)/(-2(3x^2 - 5) - 1))^2 + 4((-1(3x^2 - 5) - 1)/(-2(3x^2 - 5) - 1)) + 5) - 2) + 2) - 5) - 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 13 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(3|(2|(-2cos(2π(5(1|x - 3| + 2) + 1) - 2)) + 1| - 1) + 3| + 1)^2 + 3(3|(2|(-2cos(2π(5(1|x - 3| + 2) + 1) - 2)) + 1| - 1) + 3| + 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your ... | 365 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 1|(-3|(1|(-2|(-4(1x^2 - 1x - 2) - 2) - 3| + 3) + 3| - 2) + 2|)| - 3 where -10 ≤ x ≤ 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) = 3(-2|((-1(-3cos(1π((3(-3x^2 + 5x - 1) + 2)/(2(-3x^2 + 5x - 1) + 1)) + 3) + 3) - 2)/(-3(-3cos(1π((3(-3x^2 + 5x - 1) + 2)/(2(-3x^2 + 5x - 1) + 1)) + 3) + 3) + 2)) + 1|) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 16 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -2sin(2π(5(-5(1(-3|(-1x^2 - 5x + 2) + 2| + 1)^2 + 1(-3|(-1x^2 - 5x + 2) + 2| + 1) + 2) + 1) + 1) - 2) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 63 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (-3(1|((-3(-2(-5(1x^2 - 1x - 3)^2 + 4)^2 - 5(-5(1x^2 - 1x - 3)^2 + 4) - 1) + 3)/(1(-2(-5(1x^2 - 1x - 3)^2 + 4)^2 - 5(-5(1x^2 - 1x - 3)^2 + 4) - 1) + 3)) + 2| - 2) - 2)/(2(1|((-3(-2(-5(1x^2 - 1x - 3)^2 + 4)^2 - 5(-5(1x^2 - 1x - 3)^2 + 4) -... | 7 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5((1((-2(1sin(3π(-1(-2x^2 + 4x)) - 2) + 1) + 3)/(3(1sin(3π(-1(-2x^2 + 4x)) - 2) + 1))) - 1)/(-2((-2(1sin(3π(-1(-2x^2 + 4x)) - 2) + 1) + 3)/(3(1sin(3π(-1(-2x^2 + 4x)) - 2) + 1))))) - 4 have in the interval [-10, 10]?\n\nP... | 466 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -4(-4(1sin(3π(-3|(-3((3x - 2)/(-1x + 2))) + 3| - 2) - 2) + 3)^2 + 3(1sin(3π(-3|(-3((3x - 2)/(-1x + 2))) + 3| - 2) - 2) + 3)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 86 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 1(-5(3(1(-2(5x^2 - 1x - 1)^2 - 4(5x^2 - 1x - 1) - 5) + 4)^2 + 2(1(-2(5x^2 - 1x - 1)^2 - 4(5x^2 - 1x - 1) - 5) + 4) - 3)^2 - 5)^2 - 4(-5(3(1(-2(5x^2 - 1x - 1)^2 - 4(5x^2 - 1x - 1) - 5) + 4)^2 + 2(1(-2(5x^2 - 1x - 1)^2 - 4(5x^2 - 1x - 1) - ... | 4 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1(-3sin(3π(1|(-1|(-2(-3|x + 1| + 2) - 1) - 3|)| + 2) - 3) - 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 181 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 2(4(-1(2cos(1π((1(-3x - 4) + 2)/(-2(-3x - 4) - 1)) - 3))^2 - 2(2cos(1π((1(-3x - 4) + 2)/(-2(-3x - 4) - 1)) - 3)) - 3) - 3)^2 - 4(4(-1(2cos(1π((1(-3x - 4) + 2)/(-2(-3x - 4) - 1)) - 3))^2 - 2(2cos(1π((1(-3x - 4) + 2)/(-2(-3x - 4) - 1)) - 3)) - 3) - ... | 7 | MATH |
[
{
"content": "How many local minima does the function f(x) = -2(1(1(1sin(3π(-1|(3|x + 3| - 1)| + 2) + 1) - 1)^2 + 5(1sin(3π(-1|(3|x + 3| - 1)| + 2) + 1) - 1) - 3)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3|(4(3((3(-3sin(2π(1|x - 1| - 2) + 2) + 2) - 3)/(1(-3sin(2π(1|x - 1| - 2) + 2) + 2) + 3))^2 + 4((3(-3sin(2π(1|x - 1| - 2) + 2) + 2) - 3)/(1(-3sin(2π(1|x - 1| - 2) + 2) + 2) + 3)) - 5)^2 - 5(3((3(-3sin(2π(1|x - 1| - 2) + ... | 159 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2|((-1(2cos(1π(-3|((-2(2x - 3) + 2)/(2(2x - 3) + 2)) + 1|) + 2) + 1) + 1)/(1(2cos(1π(-3|((-2(2x - 3) + 2)/(2(2x - 3) + 2)) + 1|) + 2) + 1) + 2))| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed... | 48 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -1cos(1π(-2|(-3|(-1(-2(-1x + 3)^2 + 1) - 3) - 1|) - 2|) - 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 252 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -1(-1((-2(5((-1(-2sin(3πx) + 3) + 1)/(-3(-2sin(3πx) + 3) + 4))^2 - 3((-1(-2sin(3πx) + 3) + 1)/(-3(-2sin(3πx) + 3) + 4)) + 2))/(-2(5((-1(-2sin(3πx) + 3) + 1)/(-3(-2sin(3πx) + 3) + 4))^2 - 3((-1(-2sin(3πx) + 3) + 1)/(-3(-2sin(3πx) + 3) + 4)... | 36 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (-1(2(2|(-2(2|(-3sin(3πx - 2) + 1)|)^2 - 4(2|(-3sin(3πx - 2) + 1)|) + 2) + 3| + 3) + 2) - 3)/(-2(2(2|(-2(2|(-3sin(3πx - 2) + 1)|)^2 - 4(2|(-3sin(3πx - 2) + 1)|) + 2) + 3| + 3) + 2) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\... | 192 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -3(2e^(2(-5(2((2(2x + 2) + 1)/(1(2x + 2) - 2))^2 - 5((2(2x + 2) + 1)/(1(2x + 2) - 2)) + 3) + 3)) + 3)^2 + 4(2e^(2(-5(2((2(2x + 2) + 1)/(1(2x + 2) - 2))^2 - 5((2(2x + 2) + 1)/(1(2x + 2) - 2)) + 3) + 3)) + 3) - 3 have in the interval [-10, 10]?\n\nPrese... | 5 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 4(-1(2|((-2(-1|(-1cos(2πx) - 1)| + 3) - 2)/(1(-1|(-1cos(2πx) - 1)| + 3) + 3)) - 1| + 3)^2 - 2(2|((-2(-1|(-1cos(2πx) - 1)| + 3) - 2)/(1(-1|(-1cos(2πx) - 1)| + 3) + 3)) - 1| + 3) - 2)^2 - 1(-1(2|((-2(-1|(-1cos(2πx) - 1)| + 3) - 2)/(1(-1|(-1... | 19 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (1(3(-2e^(1(5(-2((-1x + 2)/(1x + 1)) - 5))) - 1)^2 - 1(-2e^(1(5(-2((-1x + 2)/(1x + 1)) - 5))) - 1) - 5) + 3)/(3(3(-2e^(1(5(-2((-1x + 2)/(1x + 1)) - 5))) - 1)^2 - 1(-2e^(1(5(-2((-1x + 2)/(1x + 1)) - 5))) - 1) - 5) - 1) in the interval [-10... | 12 | MATH |
[
{
"content": "How many local minima does the function f(x) = 3((-3(-2|(1|(2sin(3π((-1x + 2)/(3x + 3)) - 1) - 3) - 3| + 1) + 3| - 3) + 1)/(1(-2|(1|(2sin(3π((-1x + 2)/(3x + 3)) - 1) - 3) - 3| + 1) + 3| - 3)))^2 + 3((-3(-2|(1|(2sin(3π((-1x + 2)/(3x + 3)) - 1) - 3) - 3| + 1) + 3| - 3) + 1)/(1(-2|(1|(2sin(3π((-1x + ... | 17 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1(4((2((1(-2((-3x - 1)/(1x - 3))^2 + 2) + 1)/(2(-2((-3x - 1)/(1x - 3))^2 + 2) - 1)) + 1)/(-2((1(-2((-3x - 1)/(1x - 3))^2 + 2) + 1)/(2(-2((-3x - 1)/(1x - 3))^2 + 2) - 1)) + 1))^2)^2 - 3(4((2((1(-2((-3x - 1)/(1x - 3))^2 + 2) + 1)/(2(-2((-3x - 1)/(1x - 3... | 4 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -2e^(1(-1(1(2((1(4x^2 - 2x - 5) - 1)/(1(4x^2 - 2x - 5) + 1))^2 + 5((1(4x^2 - 2x - 5) - 1)/(1(4x^2 - 2x - 5) + 1)) - 3)^2 - 2(2((1(4x^2 - 2x - 5) - 1)/(1(4x^2 - 2x - 5) + 1))^2 + 5((1(4x^2 - 2x - 5) - 1)/(1(4x^2 - 2x - 5) + 1)) - 3) + 4) - 3)) - 1 have... | 5 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(-2cos(1π(-3(-3|(5(-1|x - 1| - 2) + 1) + 2| - 3)^2 + 4(-3|(5(-1|x - 1| - 2) + 1) + 2| - 3) + 4) + 2) + 1)^2 + 4(-2cos(1π(-3(-3|(5(-1|x - 1| - 2) + 1) + 2| - 3)^2 + 4(-3|(5(-1|x - 1| - 2) + 1) + 2| - 3) + 4) + 2) + 1) - ... | 73 | MATH |
[
{
"content": "How many local minima does the function f(x) = -3(4(3sin(2π(-2|(-1(3x + 1)^2 + 3(3x + 1) + 1) - 3|) - 1) + 1)^2 - 4(3sin(2π(-2|(-1(3x + 1)^2 + 3(3x + 1) + 1) - 3|) - 1) + 1) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 200 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -1(2(3((3(-2((1x - 1)/(2x))^2 + 1((1x - 1)/(2x)) + 3) + 1)/(-1(-2((1x - 1)/(2x))^2 + 1((1x - 1)/(2x)) + 3) - 1)) + 3) - 1)^2 + 4(2(3((3(-2((1x - 1)/(2x))^2 + 1((1x - 1)/(2x)) + 3) + 1)/(-1(-2((1x - 1)/(2x))^2 + 1((1x - 1)/(2x)) + 3) - 1)) + 3) - 1... | 5 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1(-3|(2(-5(-2(-1cos(3πx - 1))^2 + 4(-1cos(3πx - 1)) - 3)^2 + 3(-2(-1cos(3πx - 1))^2 + 4(-1cos(3πx - 1)) - 3) + 1) + 3) - 1| - 1) + 5 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) = 1(-1((-2(-3((-1(1x + 1))/(-2(1x + 1) + 1))^2 + 4((-1(1x + 1))/(-2(1x + 1) + 1)) + 5) + 3)/(-3(-3((-1(1x + 1))/(-2(1x + 1) + 1))^2 + 4((-1(1x + 1))/(-2(1x + 1) + 1)) + 5) + 2))^2 - 2((-2(-3((-1(1x + 1))/(-2(1x + 1) + 1))^2 + ... | 5 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -3((1(1|((-3(-1|(1cos(3πx + 3) - 1) + 3|) - 1)/(3(-1|(1cos(3πx + 3) - 1) + 3|) + 2)) + 2| + 1) + 2)/(2(1|((-3(-1|(1cos(3πx + 3) - 1) + 3|) - 1)/(3(-1|(1cos(3πx + 3) - 1) + 3|) + 2)) + 2| + 1) + 1))^2 - 1((1(1|((-3(-1|(1cos(3πx + 3) - 1) +... | 30 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-2(3cos(1π(4((3(2x^2 - 1x - 5))/(3(2x^2 - 1x - 5) - 1)) - 2) + 1) - 1) + 1)^2 + 1(-2(3cos(1π(4((3(2x^2 - 1x - 5))/(3(2x^2 - 1x - 5) - 1)) - 2) + 1) - 1) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in ... | 22 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1(3|((-3((-3(3|(2cos(1πx - 1) - 3) - 3| - 2) - 1)/(3(3|(2cos(1πx - 1) - 3) - 3| - 2))) + 1)/(-1((-3(3|(2cos(1πx - 1) - 3) - 3| - 2) - 1)/(3(3|(2cos(1πx - 1) - 3) - 3| - 2))) - 2)) + 1| + 3) - 5 in the interval [-10, 10].\n\n... | 20 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 1|(-3|(-1cos(1π(1(2|((2x + 3)/(-3x + 1)) + 2|)^2 + 5(2|((2x + 3)/(-3x + 1)) + 2|) - 1) + 2) + 2) - 2| + 1) + 3| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 130 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 5((-2(3sin(1π(5(-5(5x - 5))^2 - 3(-5(5x - 5)) + 3) - 2)) - 1)/(1(3sin(1π(5(-5(5x - 5))^2 - 3(-5(5x - 5)) + 3) - 2)) + 3))^2 + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 1(-3((2(-2(-2((-2x + 1)/(-3x - 3))^2 + 3((-2x + 1)/(-3x - 3)) + 1)^2 - 2(-2((-2x + 1)/(-3x - 3))^2 + 3((-2x + 1)/(-3x - 3)) + 1) + 3) - 2)/(1(-2(-2((-2x + 1)/(-3x - 3))^2 + 3((-2x + 1)/(-3x - 3)) + 1)^2 - 2(-2((-2x + 1)/(-3x - 3))^2 + 3((... | 7 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 3(-1((-3(-3(1|(-2cos(3πx - 3) - 1) + 3| + 1) - 1) - 1)/(-2(-3(1|(-2cos(3πx - 3) - 1) + 3| + 1) - 1) - 2))^2 - 1((-3(-3(1|(-2cos(3πx - 3) - 1) + 3| + 1) - 1) - 1)/(-2(-3(1|(-2cos(3πx - 3) - 1) + 3| + 1) - 1) - 2)) + 3)^2 + 3(-1((-3(-3(1|(-2cos(3πx - 3)... | 30 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2|(2((-1(-1(2|(-2sin(2πx - 1) + 1) + 3| + 3) - 3) + 1)/(3(-1(2|(-2sin(2πx - 1) + 1) + 3| + 3) - 3) + 3))^2 + 4((-1(-1(2|(-2sin(2πx - 1) + 1) + 3| + 3) - 3) + 1)/(3(-1(2|(-2sin(2πx - 1) + 1) + 3| + 3) - 3) + 3)) - 3) - 3| - ... | 40 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1(-3(3(-1(-5(-2sin(3πx - 1) + 3) + 5)^2 + 1(-5(-2sin(3πx - 1) + 3) + 5) - 5)^2 - 1(-1(-5(-2sin(3πx - 1) + 3) + 5)^2 + 1(-5(-2sin(3πx - 1) + 3) + 5) - 5) - 2))^2 + 5(-3(3(-1(-5(-2sin(3πx - 1) + 3) + 5)^2 + 1(-5(-2sin(3πx - 1)... | 54 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2(1sin(1π((-1(-3|((-2(4x - 2) + 2)/(-3(4x - 2) - 1)) - 2| + 3) + 1)/(3(-3|((-2(4x - 2) + 2)/(-3(4x - 2) - 1)) - 2| + 3) + 1)) + 3))^2 + 2(1sin(1π((-1(-3|((-2(4x - 2) + 2)/(-3(4x - 2) - 1)) - 2| + 3) + 1)/(3(-3|((-2(4x - 2... | 28 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 1(2sin(1π(3|(2|(-2(5x - 2)^2 - 4(5x - 2) - 3) - 2| - 1)| - 2) + 1) + 2)^2 + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 136 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (3(1e^(1(4(2|(-4(5x)^2 + 3(5x) + 1) - 3| + 1)^2 - 3(2|(-4(5x)^2 + 3(5x) + 1) - 3| + 1) + 1)) - 3) - 2)/(-1(1e^(1(4(2|(-4(5x)^2 + 3(5x) + 1) - 3| + 1)^2 - 3(2|(-4(5x)^2 + 3(5x) + 1) - 3| + 1) + 1)) - 3) + 2) have in the interval [-10, 10]?\n\nPresent t... | 4 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (-1((-2((2(4(-1|(-1cos(3πx + 1) + 1) + 2| + 1)^2 + 2(-1|(-1cos(3πx + 1) + 1) + 2| + 1) + 3) + 2)/(2(4(-1|(-1cos(3πx + 1) + 1) + 2| + 1)^2 + 2(-1|(-1cos(3πx + 1) + 1) + 2| + 1) + 3) + 3)) + 1)/(-2((2(4(-1|(-1cos(3πx + 1) + 1) + 2| + 1)^2 +... | 60 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1(5(1(1|(-2|(2x - 2) + 2| + 3) + 1| - 1) - 3))^2 + 2(5(1(1|(-2|(2x - 2) + 2| + 3) + 1| - 1) - 3)) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 1|(1|((2(-4(-3|(1cos(3πx - 2) + 1)| + 3)^2 + 3) - 3)/(3(-4(-3|(1cos(3πx - 2) + 1)| + 3)^2 + 3) - 1))|)| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 102 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 4(2|(-2|(1(2|(5x^2 - 5x - 3)| + 2)^2 - 3(2|(5x^2 - 5x - 3)| + 2) - 4) - 2| + 3) - 3| + 2) + 1 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) = 2((3(-5((3(-2sin(3π((1x + 1)/(-3x - 2)) + 2) + 1) + 1)/(-1(-2sin(3π((1x + 1)/(-3x - 2)) + 2) + 1) + 2))^2 + 3) - 3)/(2(-5((3(-2sin(3π((1x + 1)/(-3x - 2)) + 2) + 1) + 1)/(-1(-2sin(3π((1x + 1)/(-3x - 2)) + 2) + 1) + 2))^2 + 3) + 1))^2 + 4((3(-5((3(-... | 12 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 4(1sin(3π(4(-5(-1|(-1|x + 2| + 2) + 1| - 2) - 5)^2 - 4(-5(-1|(-1|x + 2| + 2) + 1| - 2) - 5) - 5) + 3) - 2) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 371 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (-1((2(-1|(-3|(-1sin(2π(-4x - 3)) + 2) - 2|) - 3|) + 2)/(3(-1|(-3|(-1sin(2π(-4x - 3)) + 2) - 2|) - 3|) + 3)) - 1)/(-2((2(-1|(-3|(-1sin(2π(-4x - 3)) + 2) - 2|) - 3|) + 2)/(3(-1|(-3|(-1sin(2π(-4x - 3)) + 2) - 2|) - 3|) + 3)) + 3) where -10 ... | 268 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (-1(-2|(-2cos(3π(4(2(-3x^2 + 2x - 4) - 2) + 1)) - 3) - 1| + 3) + 1)/(2(-2|(-2cos(3π(4(2(-3x^2 + 2x - 4) - 2) + 1)) - 3) - 1| + 3) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 364 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 1(5(-1(-1|(-4((2x + 3)/(3x))^2 + 4((2x + 3)/(3x)) + 3) + 1| + 2)^2 + 1(-1|(-4((2x + 3)/(3x))^2 + 4((2x + 3)/(3x)) + 3) + 1| + 2) - 5)^2 + 5(-1(-1|(-4((2x + 3)/(3x))^2 + 4((2x + 3)/(3x)) + 3) + 1| + 2)^2 + 1(-1|(-4((2x + 3)/(3x))^2 + 4((2x + 3)/(3x... | 6 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(3cos(1π(-3(-4(2|(-5x - 3) + 3| - 1)^2 + 2(2|(-5x - 3) + 3| - 1) + 4)^2 + 4(-4(2|(-5x - 3) + 3| - 1)^2 + 2(2|(-5x - 3) + 3| - 1) + 4) - 4) - 3)) + 3)/(1(3cos(1π(-3(-4(2|(-5x - 3) + 3| - 1)^2 + 2(2|(-5x - 3) + 3| - 1) + ... | 17 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 2sin(1π((-2(2(-1(-4((-2x - 3)/(-3x - 2))^2 + 5((-2x - 3)/(-3x - 2)) + 4) + 1)^2 - 3(-1(-4((-2x - 3)/(-3x - 2))^2 + 5((-2x - 3)/(-3x - 2)) + 4) + 1) - 2) + 2)/(-1(2(-1(-4((-2x - 3)/(-3x - 2))^2 + 5((-2x - 3)/(-3x - 2)) + 4) + 1)^2 - 3(-1(-4((-2x - 3)/(... | 5 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-3(4(-1(-1sin(2π(-5(5x - 5) + 5) - 2)))^2 + 2(-1(-1sin(2π(-5(5x - 5) + 5) - 2))) - 5) + 2)/(-3(4(-1(-1sin(2π(-5(5x - 5) + 5) - 2)))^2 + 2(-1(-1sin(2π(-5(5x - 5) + 5) - 2))) - 5) + 1) have in the interval [-10, 10]?\n\nPr... | 164 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 2(-1cos(2π((-2(-1(-1|(1|x - 1| - 1) - 2| + 2)^2 - 4(-1|(1|x - 1| - 1) - 2| + 2)) - 3)/(-2(-1(-1|(1|x - 1| - 1) - 2| + 2)^2 - 4(-1|(1|x - 1| - 1) - 2| + 2)) + 3)) - 2) - 3)^2 + 4(-1cos(2π((-2(-1(-1|(1|x - 1| - 1) - 2| + 2)^2 - 4(-1|(1|x - ... | 150 | MATH |
[
{
"content": "How many local minima does the function f(x) = 3|(-1(4(-1((2(-2sin(2πx + 2) - 2) - 1)/(-1(-2sin(2πx + 2) - 2) - 2)) - 5) - 5)^2 - 3(4(-1((2(-2sin(2πx + 2) - 2) - 1)/(-1(-2sin(2πx + 2) - 2) - 2)) - 5) - 5) - 4)| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 99 | MATH |
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