messages listlengths 1 1 | ground_truth stringclasses 47 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (-3((-3(-2sin(1πx - 2) + 2) + 2)/(2(-2sin(1πx - 2) + 2) + 1)) + 1)/(-2((-3(-2sin(1πx - 2) + 2) + 2)/(2(-2sin(1πx - 2) + 2) + 1)) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex ... | 8 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = -2(2e^(2(1|x + 2| + 2)))^2 + 2(2e^(2(1|x + 2| + 2))) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -2|(-1(-1sin(2πx - 2) - 2) - 4) + 1| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 5((-2(3x - 4) + 1)/(-1(3x - 4) + 3))^2 + 4((-2(3x - 4) + 1)/(-1(3x - 4) + 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = 3e^(-2(-3|((2x - 2)/(3x - 1)) - 3| - 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = (2(-1(-3x)^2 + 5(-3x) - 1) + 2)/(2(-1(-3x)^2 + 5(-3x) - 1) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = 5(2e^(2((-2x)/(1x + 2))) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2(-1(-1sin(1πx - 2) + 1) + 5) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2cos(2π(-1|(2|x - 1| + 1) - 2| + 1) - 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3sin(2π(5(2|x + 2| + 3)^2 + 1(2|x + 2| + 3) + 4)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 5(5(2|x - 2| - 3)^2 + 3(2|x - 2| - 3) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 5(-3(-5x^2 - 1x + 3)^2 + 3(-5x^2 - 1x + 3) - 4)^2 - 1(-3(-5x^2 - 1x + 3)^2 + 3(-5x^2 - 1x + 3) - 4) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -5(-3sin(3π(1|x - 3| + 1) - 1)) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -2sin(3π((3(-4x^2 + 2x - 4) + 1)/(3(-4x^2 + 2x - 4) - 2))) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2|(-2sin(1π((1x + 1)/(-2x + 1)) - 3) + 2) + 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 2|(-2(-1|x - 2|)^2 + 3(-1|x - 2|) - 3) - 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -5(1cos(2π(-4x^2 - 4x + 5)))^2 + 5(1cos(2π(-4x^2 - 4x + 5))) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3((-2(3cos(1πx - 2) - 2) + 1)/(-1(3cos(1πx - 2) - 2))) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2(3cos(1π(-5x^2 + 5x + 3) - 3) + 3)^2 - 3(3cos(1π(-5x^2 + 5x + 3) - 3) + 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | -9 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2cos(1π(2((-2x)/(-1x + 3)) - 1) - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = -3|(1e^(2(-5x^2 + 4x + 2)) - 2) - 1| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -4(2(3|x + 3| - 3)^2 + 4(3|x + 3| - 3) + 4) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1|(-1e^(2(2|x - 2| + 3))) - 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -2cos(3π(3|(-1|x + 1| + 3) + 3| - 1) - 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1(-3sin(3π(1|x + 1| - 3)) - 1) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = 4((2(3x^2 - 3x - 2) + 2)/(2(3x^2 - 3x - 2) - 1)) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1|(2sin(3π((2x + 2)/(1x - 2)))) + 2| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3cos(2π((-2(3|x - 2| + 1) + 1)/(-2(3|x - 2| + 1) + 3)) - 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1|(2|(3x^2 + 2x - 3) - 3|) - 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = (-1((2(-1x^2 + 2x - 4) - 1)/(-2(-1x^2 + 2x - 4) - 1)) - 1)/(1((2(-1x^2 + 2x - 4) - 1)/(-2(-1x^2 + 2x - 4) - 1)) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 1 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -5(1sin(3π(-2x^2 - 4x + 1)))^2 - 2(1sin(3π(-2x^2 - 4x + 1))) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 2cos(3π(1(1x^2 + 2x - 5)) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = (-2(-1(1x^2 - 1x + 1) - 4) + 2)/(1(-1(1x^2 - 1x + 1) - 4) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -2e^(-1(3|(-5x^2 - 2x - 2) + 3| + 1)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -3|(1|(3cos(2πx - 2) + 1) - 2| + 2) - 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -3e^(2(1(4x + 5)^2 + 1(4x + 5) - 2)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = 2|(-1e^(2(4x - 5))) + 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = (-1((-1(-2x^2 - 1) - 1)/(1(-2x^2 - 1) + 2)) + 1)/(-3((-1(-2x^2 - 1) - 1)/(1(-2x^2 - 1) + 2)) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -5(2(-1sin(3πx) + 2) + 2) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = -2(-1|(1x^2 - 1x - 1) + 2| - 3)^2 - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -1sin(1π(3(-1|x - 2| + 1) + 4) + 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = (-3(-3(-3|x - 2| + 1) - 1) - 3)/(1(-3(-3|x - 2| + 1) - 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = -2|(2e^(1((3x - 3)/(1x))) - 1) + 3| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 4(-5(-3sin(3πx + 2) + 2)^2 - 3(-3sin(3πx + 2) + 2) - 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2(-1e^(-2(-2x^2 + 5x - 2)) - 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -1(-5(2sin(3πx) - 1) - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = -2e^(1(1|(3|x - 3| + 2) - 2| + 3)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1e^(2(-2|((3x - 2)/(-3x - 3)) - 3| - 1)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = (-2((3(-1x^2 + 5x + 1) + 3)/(1(-1x^2 + 5x + 1) - 3)) - 1)/(-1((3(-1x^2 + 5x + 1) + 3)/(1(-1x^2 + 5x + 1) - 3)) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 2 | MATH |
[
{
"content": "How many local minima does the function f(x) = (-2(-1(3|x + 3| - 2) + 3) - 1)/(2(-1(3|x + 3| - 2) + 3) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = -2e^(-2(1(3x^2 - 5x + 3) - 4)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 3((3(1cos(3πx - 1)))/(-1(1cos(3πx - 1)))) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 4(-5(-1sin(3πx - 1) + 3)^2 - 1(-1sin(3πx - 1) + 3) - 1)^2 + 4(-5(-1sin(3πx - 1) + 3)^2 - 1(-1sin(3πx - 1) + 3) - 1) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxe... | 10 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (-2(2|(1x^2 + 3x + 3) + 1| + 3) + 2)/(-2(2|(1x^2 + 3x + 3) + 1| + 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2cos(2π(5(2x^2 + 1x + 1) + 5) - 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 1((3(5x^2 - 4x) + 2)/(3(5x^2 - 4x) + 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -2(5(4x^2 - 4x - 2)^2 + 5(4x^2 - 4x - 2) - 1)^2 - 4(5(4x^2 - 4x - 2)^2 + 5(4x^2 - 4x - 2) - 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 1((-3((-3x - 3)/(-1x + 3)) - 1)/(-1((-3x - 3)/(-1x + 3)) - 1))^2 - 3((-3((-3x - 3)/(-1x + 3)) - 1)/(-1((-3x - 3)/(-1x + 3)) - 1)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = (2(4(-3x^2 - 3x - 4)^2 + 1(-3x^2 - 3x - 4) + 4) - 2)/(-1(4(-3x^2 - 3x - 4)^2 + 1(-3x^2 - 3x - 4) + 4) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = (-3((1(1x^2 + 4x) - 1)/(2(1x^2 + 4x) - 1)) + 3)/(2((1(1x^2 + 4x) - 1)/(2(1x^2 + 4x) - 1))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1(3e^(-1(1|x - 2|)) + 1)^2 + 5(3e^(-1(1|x - 2|)) + 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (3((-2(2cos(2πx + 3) - 3) - 2)/(3(2cos(2πx + 3) - 3) - 2)) + 2)/(2((-2(2cos(2πx + 3) - 3) - 2)/(3(2cos(2πx + 3) - 3) - 2)) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex forma... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (-3(5(5x^2 - 4)^2 - 2(5x^2 - 4) + 2) + 1)/(1(5(5x^2 - 4)^2 - 2(5x^2 - 4) + 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 1 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = 1(2sin(3π(1x^2 + 2x) + 2) + 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 559 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -2(1cos(1π(3|x| + 1) + 2) - 1)^2 + 2(1cos(1π(3|x| + 1) + 2) - 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = 2((-2(-3e^(1x) - 1) - 3)/(3(-3e^(1x) - 1) + 3))^2 - 4((-2(-3e^(1x) - 1) - 3)/(3(-3e^(1x) - 1) + 3)) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | -3 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1|(-2sin(1π(-3x + 4) + 3) + 3) + 2| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2sin(2π(1|(3|x - 3| - 2) + 1| - 3) - 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = 2e^(2(-1|((1x + 1)/(1x - 3)) - 1| - 3)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -1(-4(-2sin(2πx + 2)) - 4)^2 - 4(-4(-2sin(2πx + 2)) - 4) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "How many local minima does the function f(x) = (1(2|((1x + 3)/(2x)) + 3| - 1) + 2)/(-1(2|((1x + 3)/(2x)) + 3| - 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -1|(1(1x^2 + 5) - 5) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = 5((3((3x)/(3x + 1)) + 3)/(1((3x)/(3x + 1)) + 1))^2 + 5((3((3x)/(3x + 1)) + 3)/(1((3x)/(3x + 1)) + 1)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 1 | MATH |
[
{
"content": "How many local minima does the function f(x) = (-2((-1(-1x^2 - 1x) - 3)/(-2(-1x^2 - 1x) + 3)) + 1)/(2((-1(-1x^2 - 1x) - 3)/(-2(-1x^2 - 1x) + 3))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = (-2(2e^(1(-4x^2 + 3x - 2)) - 1) - 1)/(-1(2e^(1(-4x^2 + 3x - 2)) - 1) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 2sin(2π(-4((3x + 1)/(-3x + 2)) - 1) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 2e^(-1(1|((-2x - 1)/(2x + 2))| + 1)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -1sin(1π(-1(-2|x - 3| - 2) - 1) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -9 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (3(3sin(2π((1x + 1)/(3x + 2)) - 3)) + 2)/(-3(3sin(2π((1x + 1)/(3x + 2)) - 3))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-3(1|(1cos(2πx + 2) + 2) + 3|) - 1)/(-2(1|(1cos(2πx + 2) + 2) + 3|) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | -9 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = 1((1((3x - 3)/(-2x)))/(1((3x - 3)/(-2x)) - 3))^2 - 1((1((3x - 3)/(-2x)))/(1((3x - 3)/(-2x)) - 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -3sin(1π((-2((-1x - 2)/(-2x + 1)) + 3)/(3((-1x - 2)/(-2x + 1)) + 2)) + 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | -1 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2cos(2π((2(2|x + 3| + 1) - 2)/(-3(2|x + 3| + 1) - 2))) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 5(-3|(2cos(2πx + 2) + 1) - 3| + 2)^2 - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = 2sin(2π(3(-4x^2 + 3x + 3) - 5) + 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (-2(-2(3cos(3πx + 3)) + 3) - 1)/(3(-2(3cos(3πx + 3)) + 3) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 3(1sin(3π(-1x^2 - 5x + 5) - 3) + 2) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -2|(-2cos(2π(3|x| - 3) - 1) - 3)| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 4(2(2sin(1πx + 3) + 2) + 2) - 5 in the interval [-10, 10]. Round to the nearest integer.\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(1|(3x + 4)| - 3)^2 - 2(1|(3x + 4)| - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 5(4(-3sin(1πx + 3))^2 + 3(-3sin(1πx + 3)) - 5)^2 + 3(4(-3sin(1πx + 3))^2 + 3(-3sin(1πx + 3)) - 5) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 10 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 2|(4(4x^2 - 2)^2 + 1(4x^2 - 2) - 3) - 2| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1(2e^(1(1x^2 + 2x - 5)) - 1)^2 - 5(2e^(1(1x^2 + 2x - 5)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "How many local minima does the function f(x) = -3(2|(5x^2 + 2x + 2) + 2| + 3)^2 - 4(2|(5x^2 + 2x + 2) + 2| + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (2(-3cos(2π((3x + 2)/(-1x - 1)))))/(1(-3cos(2π((3x + 2)/(-1x - 1)))) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 1|(-4((3x - 3)/(2x)) + 1) - 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 4(-1(-3|x + 1| + 2)^2 - 1(-3|x + 1| + 2) + 2)^2 + 1(-1(-3|x + 1| + 2)^2 - 1(-3|x + 1| + 2) + 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Y... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 2|(-5(1x^2 - 1x + 5)^2 - 4(1x^2 - 1x + 5) + 5)| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3(2(-2cos(3πx - 1) + 2)^2 - 2(-2cos(3πx - 1) + 2) - 4) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = -1(1|(5x^2 - 4) - 1| - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
End of preview. Expand
in Data Studio
No dataset card yet
- Downloads last month
- 6