messages listlengths 1 1 | ground_truth stringclasses 42 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = -5(3(-4(1sin(2π(3((2x - 3)/(2x + 2)) - 4) - 3) - 3)^2 - 2(1sin(2π(3((2x - 3)/(2x + 2)) - 4) - 3) - 3) - 2) + 4)^2 + 3(3(-4(1sin(2π(3((2x - 3)/(2x + 2)) - 4) - 3) - 3)^2 - 2(1sin(2π(3((2x - 3)/(2x + 2)) - 4) - 3) - 3) - 2) + 4... | 63 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = 2|(1(-2|((3(-3(1x^2 - 1) - 2) - 1)/(-3(-3(1x^2 - 1) - 2) - 3)) + 1| + 3) - 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 average of all x-coordinates of local extrema of the function f(x) = (-3(3e^(-1(-1(-3|(1(-4x - 1)^2 - 3(-4x - 1) + 2) - 2| + 2) + 3)) + 1) + 3)/(2(3e^(-1(-1(-3|(1(-4x - 1)^2 - 3(-4x - 1) + 2) - 2| + 2) + 3)) + 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (1((-3(-3sin(1π((3(-4(2x - 5)) + 3)/(-1(-4(2x - 5)) - 2)) + 1) - 3) + 2)/(-2(-3sin(1π((3(-4(2x - 5)) + 3)/(-1(-4(2x - 5)) - 2)) + 1) - 3) + 3)) + 3)/(-2((-3(-3sin(1π((3(-4(2x - 5)) + 3)/(-1(-4(2x - 5)) - 2... | 1 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (-3(4((-3(-2cos(1π(1|((2x - 1)/(1x))| - 3) - 3) - 1) + 1)/(1(-2cos(1π(1|((2x - 1)/(1x))| - 3) - 3) - 1) - 2))^2 - 2((-3(-2cos(1π(1|((2x - 1)/(1x))| - 3) - 3) - 1) + 1)/(1(-2cos(1π(1|((2x - 1)/(1x))| - 3) - 3) - 1) - 2)) - 5... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1cos(2π(-4((3(-1|(4(-2|x - 1| - 2) + 4) - 3|))/(-2(-1|(4(-2|x - 1| - 2) + 4) - 3|) - 3)) + 5)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | -1 | MATH |
[
{
"content": "How many local minima does the function f(x) = 2|(3(-2sin(1π(-1|(2(-2x + 3) - 3) + 1|)) + 3)^2 - 4(-2sin(1π(-1|(2(-2x + 3) - 3) + 1|)) + 3) - 5) - 1| + 3 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) = (-2(2|((2(2(-2sin(2π(1x^2 - 5x - 3) - 1) + 3)^2 - 1(-2sin(2π(1x^2 - 5x - 3) - 1) + 3) + 1) + 2)/(3(2(-2sin(2π(1x^2 - 5x - 3) - 1) + 3)^2 - 1(-2sin(2π(1x^2 - 5x - 3) - 1) + 3) + 1) + 1)) - 2|) - 2)/(-1(2|((2(2(-2sin(2π(1x^... | -1 | MATH |
[
{
"content": "How many local minima does the function f(x) = -4(2e^(-1(4((-3(-3(1|x - 3| + 1)^2 - 5(1|x - 3| + 1) + 3) + 3)/(-2(-3(1|x - 3| + 1)^2 - 5(1|x - 3| + 1) + 3) - 3)) - 4))) + 4 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) = -1(3(-4(1(2|(2|x + 1| - 2)| + 1)^2 + 3(2|(2|x + 1| - 2)| + 1) - 5)^2 - 4(1(2|(2|x + 1| - 2)| + 1)^2 + 3(2|(2|x + 1| - 2)| + 1) - 5) - 3) - 5)^2 + 1(3(-4(1(2|(2|x + 1| - 2)| + 1)^2 + 3(2|(2|x + 1| - 2)| + 1) - 5)^2 - 4(1(2|(2|x + 1| ... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -1(-1cos(2π((-3(-2((1(-2|x + 2| + 3) - 1)/(3(-2|x + 2| + 3) + 3)) - 2) + 2)/(-2(-2((1(-2|x + 2| + 3) - 1)/(3(-2|x + 2| + 3) + 3)) - 2))) + 3) - 3)^2 + 5 in the interval [-10, 10]. Round to the nearest inte... | -4 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = (-2((-1(3(1(-1|((-3x - 3)/(1x)) - 2| + 3) + 4) - 4) - 1)/(-3(3(1(-1|((-3x - 3)/(1x)) - 2| + 3) + 4) - 4) + 2)) + 1)/(3((-1(3(1(-1|((-3x - 3)/(1x)) - 2| + 3) + 4) - 4) - 1)/(-3(3(1(-1|((-3x - 3)/(1x)) - 2| + 3) + 4) - 4) + 2)) + 1) ... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = -1((1((-1((2((1(-2x^2 + 1x + 4) + 2)/(-1(-2x^2 + 1x + 4))) + 2)/(-2((1(-2x^2 + 1x + 4) + 2)/(-1(-2x^2 + 1x + 4))) + 1)) + 2)/(-3((2((1(-2x^2 + 1x + 4) + 2)/(-1(-2x^2 + 1x + 4))) + 2)/(-2((1(-2x^2 + 1x + 4) + 2)/(-1(-2x^2 + 1x + 4))... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (-2(2|(-2|(1(-4((-2x)/(1x + 3)) + 2)^2 + 5(-4((-2x)/(1x + 3)) + 2) + 4) - 2| + 2)| - 2) + 2)/(2(2|(-2|(1(-4((-2x)/(1x + 3)) + 2)^2 + 5(-4((-2x)/(1x + 3)) + 2) + 4) - 2| + 2)| - 2) - 3) in the interval [-10,... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 3|(-2(2(1sin(2π((1((3x - 3)/(-1x + 3)) + 3)/(2((3x - 3)/(-1x + 3)) + 3)) - 2) + 2)^2 + 2(1sin(2π((1((3x - 3)/(-1x + 3)) + 3)/(2((3x - 3)/(-1x + 3)) + 3)) - 2) + 2) - 1)^2 + 5(2(1sin(2π((1((3x - 3)/(-1x + 3)) + 3)/(2((3x - ... | 3 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = (-2(2((-3(1(-3(1x^2 + 3x - 4)^2 - 3(1x^2 + 3x - 4) - 2)^2 - 3(-3(1x^2 + 3x - 4)^2 - 3(1x^2 + 3x - 4) - 2) - 2))/(1(1(-3(1x^2 + 3x - 4)^2 - 3(1x^2 + 3x - 4) - 2)^2 - 3(-3(1x^2 + 3x - 4)^2 - 3(1x^2 + 3x - 4) - 2) - 2) + 1))^2 +... | 2 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = 2|(-3|(-1e^(1(2(3(1x^2 + 1x + 3)^2 + 4(1x^2 + 1x + 3) - 2) - 2)))| - 1) - 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 leftmost local maximum of the function f(x) = -1(-1|(1cos(1π(-2|(-1|(-4x + 5) - 3|) + 3| - 1)) - 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 local maximum with the largest y-value of the function f(x) = -4(2(-2|(-2((-3((2x - 3)/(3x + 2)) + 3)/(-3((2x - 3)/(3x + 2)) - 2))^2 - 5((-3((2x - 3)/(3x + 2)) + 3)/(-3((2x - 3)/(3x + 2)) - 2)) + 4) + 2| - 2) + 5)^2 + 4(2(-2|(-2((-3((2x - 3)/(3x + 2)) + 3)/(-3((2x - 3)... | -1 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (-1(-3|((-1(-4(-1(2x^2 + 1x + 4)^2 - 2) - 1) + 3)/(2(-4(-1(2x^2 + 1x + 4)^2 - 2) - 1) - 1))| + 3) - 2)/(-1(-3|((-1(-4(-1(2x^2 + 1x + 4)^2 - 2) - 1) + 3)/(2(-4(-1(2x^2 + 1x + 4)^2 - 2) - 1) - 1))| + 3) - 1) have in the interval [-10, 10]?\n\nPresent th... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 2|(-2(-2(-1|(1(1cos(2πx + 2) + 1) + 2) + 1| - 1) - 4)^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"
}
] | 10 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -3((-3(-3(-3|(-1(-3sin(1πx - 1) - 2) - 1) - 2| + 1)^2 - 1(-3|(-1(-3sin(1πx - 1) - 2) - 1) - 2| + 1) - 5) + 1)/(-1(-3(-3|(-1(-3sin(1πx - 1) - 2) - 1) - 2| + 1)^2 - 1(-3|(-1(-3sin(1πx - 1) - 2) - 1) - 2| + 1) - 5) + 2)) + 5 i... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -4((2(-4(1|(1(2sin(2πx + 3) + 1)^2 - 1(2sin(2πx + 3) + 1) + 4) + 3| + 1) - 2) - 2)/(-1(-4(1|(1(2sin(2πx + 3) + 1)^2 - 1(2sin(2πx + 3) + 1) + 4) + 3| + 1) - 2) + 2)) - 3 in the interval [-10, 10]. Round to the nearest integ... | 9 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (-3((1((1(-1e^(1(4(-2|x - 3| - 1) + 4)) - 3) + 2)/(1(-1e^(1(4(-2|x - 3| - 1) + 4)) - 3) + 1)))/(-2((1(-1e^(1(4(-2|x - 3| - 1) + 4)) - 3) + 2)/(1(-1e^(1(4(-2|x - 3| - 1) + 4)) - 3) + 1)) + 1)))/(2((1((1(-1e^... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2(2|(2(-2|(-1(3e^(-2x) - 2) + 3) + 1|)^2 - 4(-2|(-1(3e^(-2x) - 2) + 3) + 1|) - 5) - 1| + 3)^2 - 3(2|(2(-2|(-1(3e^(-2x) - 2) + 3) + 1|)^2 - 4(-2|(-1(3e^(-2x) - 2) + 3) + 1|) - 5) - 1| + 3) - 1 in the interval [-10, 10]. Ro... | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2(-3(2e^(1(-1(-5((-1x + 3)/(1x)) - 1)^2 + 4(-5((-1x + 3)/(1x)) - 1) + 4)) + 3)^2 + 2(2e^(1(-1(-5((-1x + 3)/(1x)) - 1)^2 + 4(-5((-1x + 3)/(1x)) - 1) + 4)) + 3) + 3)^2 in the interval [-10, 10]. Round to the nearest intege... | -4 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -1cos(3π(3((3(1(-4(1x^2 + 5x - 3)^2 + 2(1x^2 + 5x - 3) - 1)^2 + 5(-4(1x^2 + 5x - 3)^2 + 2(1x^2 + 5x - 3) - 1) - 4) - 1)/(3(1(-4(1x^2 + 5x - 3)^2 + 2(1x^2 + 5x - 3) - 1)^2 + 5(-4(1x^2 + 5x - 3)^2 + 2(1x^2 + 5x - 3) - 1) - ... | -2 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1e^(1(-1(-5(2(2|(-2|x - 3| + 2) - 3| - 3)^2 - 3(2|(-2|x - 3| + 2) - 3| - 3) - 1) - 5)^2 - 1(-5(2(2|(-2|x - 3| + 2) - 3| - 3)^2 - 3(2|(-2|x - 3| + 2) - 3| - 3) - 1) - 5))) - 2 in the interval [-10, 10]. Round to the neare... | 3 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = -4((1(2|(1|(1|((1x + 3)/(-1x)) + 2| - 2)| - 1) + 3| + 3) + 2)/(1(2|(1|(1|((1x + 3)/(-1x)) + 2| - 2)| - 1) + 3| + 3) - 2)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 4((3(1(1((3(-2x + 1))/(-3(-2x + 1) - 2)) + 4)^2 - 1(1((3(-2x + 1))/(-3(-2x + 1) - 2)) + 4) - 5) + 2)/(1(1(1((3(-2x + 1))/(-3(-2x + 1) - 2)) + 4)^2 - 1(1((3(-2x + 1))/(-3(-2x + 1) - 2)) + 4) - 5) - 3)) + 5 in the interval [... | 1 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -5((-3(5(-3((2((1x - 1)/(2x + 3)) + 3)/(2((1x - 1)/(2x + 3)) + 2))^2 + 5((2((1x - 1)/(2x + 3)) + 3)/(2((1x - 1)/(2x + 3)) + 2)) - 4) + 5) - 1)/(3(5(-3((2((1x - 1)/(2x + 3)) + 3)/(2((1x - 1)/(2x + 3)) + 2))^2 + 5((2((1x - ... | -1 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = -2|(-4((1(3cos(1π(3(3x)^2 + 3(3x) - 1) - 1) + 3) + 2)/(3(3cos(1π(3(3x)^2 + 3(3x) - 1) - 1) + 3) - 1))^2 + 2((1(3cos(1π(3(3x)^2 + 3(3x) - 1) - 1) + 3) + 2)/(3(3cos(1π(3(3x)^2 + 3(3x) - 1) - 1) + 3) - 1)) - 4) - 3| - 2 have in ... | 452 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = 5(2|(1|(5((-3(-1x + 3))/(-1(-1x + 3) + 2)) - 1)| + 3) + 1| - 3)^2 - 2(2|(1|(5((-3(-1x + 3))/(-1(-1x + 3) + 2)) - 1)| + 3) + 1| - 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: ... | 3 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = (2((-3(-1|(-1(1|(3|x| + 1) + 3| + 2) + 2) - 3| - 1) + 2)/(-1(-1|(-1(1|(3|x| + 1) + 3| + 2) + 2) - 3| - 1) + 2)) - 1)/(-3((-3(-1|(-1(1|(3|x| + 1) + 3| + 2) + 2) - 3| - 1) + 2)/(-1(-1|(-1(1|(3|x| + 1) + 3| + 2) + 2) - 3| - 1) + 2))) i... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (-2(3sin(1π(-2|(-2(-2(-5x)^2 - 3(-5x) + 4)^2 - 4(-2(-5x)^2 - 3(-5x) + 4) + 3) - 1| - 2) - 1) + 3) + 3)/(1(3sin(1π(-2|(-2(-2(-5x)^2 - 3(-5x) + 4)^2 - 4(-2(-5x)^2 - 3(-5x) + 4) + 3) - 1| - 2) - 1) + 3) - 3) in the interval [... | 1 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 1|((-2(-3e^(-1(-5((3((-2x - 3)/(-1x + 3)) - 2)/(1((-2x - 3)/(-1x + 3))))^2 - 3((3((-2x - 3)/(-1x + 3)) - 2)/(1((-2x - 3)/(-1x + 3)))) - 1)) + 2) + 2)/(-3(-3e^(-1(-5((3((-2x - 3)/(-1x + 3)) - 2)/(1((-2x - 3)... | -3 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2e^(1(4(-4(2(2|(-3|x| + 3) - 2| - 3) + 2)^2 - 4(2(2|(-3|x| + 3) - 2| - 3) + 2))^2 - 3(-4(2(2|(-3|x| + 3) - 2| - 3) + 2)^2 - 4(2(2|(-3|x| + 3) - 2| - 3) + 2)) - 4)) in the interval [-10, 10]. Round to the nearest integer... | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2|(-1(-1cos(3π(-1|((1(-1x + 4) - 2)/(-2(-1x + 4) + 3)) - 3| - 3) - 1) - 3) + 4) - 3| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 3 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (-3(-3(2e^(1(3|(-1(-1x) - 3) + 2| + 1)) - 3) + 5) - 3)/(2(-3(2e^(1(3|(-1(-1x) - 3) + 2| + 1)) - 3) + 5) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = (-3(3cos(2π((-1(-2|(-5(3x^2 + 5x - 1) - 2) + 3| - 2) - 2)/(3(-2|(-5(3x^2 + 5x - 1) - 2) + 3| - 2) - 2)) - 1) - 1) - 3)/(2(3cos(2π((-1(-2|(-5(3x^2 + 5x - 1) - 2) + 3| - 2) - 2)/(3(-2|(-5(3x^2 + 5x - 1) - 2) + 3| - 2) - 2)) - 1) - 1) ... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1(2|(1(-4(-5((3x + 2)/(-3x)) + 2)^2 + 4)^2 + 4(-4(-5((3x + 2)/(-3x)) + 2)^2 + 4) + 1) - 2|)^2 - 4(2|(1(-4(-5((3x + 2)/(-3x)) + 2)^2 + 4)^2 + 4(-4(-5((3x + 2)/(-3x)) + 2)^2 + 4) + 1) - 2|) + 1 in the interva... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (2(-1(3e^(1(-4(1(-2|x| + 1) + 3) + 1)) - 2)^2 - 4(3e^(1(-4(1(-2|x| + 1) + 3) + 1)) - 2) + 3) - 3)/(1(-1(3e^(1(-4(1(-2|x| + 1) + 3) + 1)) - 2)^2 - 4(3e^(1(-4(1(-2|x| + 1) + 3) + 1)) - 2) + 3) + 1) in the inte... | 4 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 5(2|((-2(5(1|(-1x^2 - 2x - 3) + 2| + 3) - 4) + 3)/(2(5(1|(-1x^2 - 2x - 3) + 2| + 3) - 4))) - 2| + 1) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = -1(-3|(-1|((-3((-1(2x^2 + 2x + 5) + 3)/(-1(2x^2 + 2x + 5) + 2)) - 1)/(1((-1(2x^2 + 2x + 5) + 3)/(-1(2x^2 + 2x + 5) + 2)) - 3))|) + 3| - 1) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex ... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2|(-4(-4(-2|(-2e^(1(2x^2 + 4x + 5)) + 1) + 3|))^2 + 3(-4(-2|(-2e^(1(2x^2 + 4x + 5)) + 1) + 3|)) + 5) + 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format... | 6 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = -5(3((-1(-2e^(-1((3((-1x - 2)/(-2x - 1)))/(-2((-1x - 2)/(-2x - 1)) - 2))) - 3) + 3)/(3(-2e^(-1((3((-1x - 2)/(-2x - 1)))/(-2((-1x - 2)/(-2x - 1)) - 2))) - 3) - 2))^2 + 3((-1(-2e^(-1((3((-1x - 2)/(-2x - 1)))/(-2((-1x - 2)/(-2x - 1)) -... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = (1(3|((1(2e^(-1(1(2x - 5)^2 + 5))) - 1)/(3(2e^(-1(1(2x - 5)^2 + 5))) + 2))| - 2) - 2)/(-1(3|((1(2e^(-1(1(2x - 5)^2 + 5))) - 1)/(3(2e^(-1(1(2x - 5)^2 + 5))) + 2))| - 2) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\... | 0 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1(-4((-3(4(-1|(3cos(2πx + 1) + 1) - 3| - 2)^2 - 3(-1|(3cos(2πx + 1) + 1) - 3| - 2) - 1) + 2)/(1(4(-1|(3cos(2πx + 1) + 1) - 3| - 2)^2 - 3(-1|(3cos(2πx + 1) + 1) - 3| - 2) - 1) + 1))^2 + 3((-3(4(-1|(3cos(2πx + 1) + 1) - 3| - 2)^2 - 3(-1|(3cos(2πx + 1) ... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3sin(2π(1|(-2|((-3(1|(2x + 2) + 3| - 3) - 1)/(-2(1|(2x + 2) + 3| - 3) + 3)) - 1| + 2) - 1|) - 2) - 1 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 average of all x-coordinates of local minima of the function f(x) = -3(-2(-2|(-2cos(3π((-3((3x)/(1x + 1)) + 2)/(1((3x)/(1x + 1)) + 1)) - 2) - 1) - 1| - 1)^2 + 4(-2|(-2cos(3π((-3((3x)/(1x + 1)) + 2)/(1((3x)/(1x + 1)) + 1)) - 2) - 1) - 1| - 1) + 1)^2 + 5(-2(-2|(-2cos(3π((-3((3x)/(1x + 1)) +... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = (3((-3(-2(-1(1(-5x^2 + 5x + 1) - 5))^2 + 5(-1(1(-5x^2 + 5x + 1) - 5)) + 5) + 3)/(1(-2(-1(1(-5x^2 + 5x + 1) - 5))^2 + 5(-1(1(-5x^2 + 5x + 1) - 5)) + 5) + 2)) - 1)/(-2((-3(-2(-1(1(-5x^2 + 5x + 1) - 5))^2 + 5(-1(1(-5x^2 + 5x + 1) - 5))... | 0 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (-3((-1((3((-3(-3(5x - 3)^2 - 4(5x - 3) + 2) - 1)/(-2(-3(5x - 3)^2 - 4(5x - 3) + 2) - 3)) - 2)/(-3((-3(-3(5x - 3)^2 - 4(5x - 3) + 2) - 1)/(-2(-3(5x - 3)^2 - 4(5x - 3) + 2) - 3)) - 1)) + 1)/(2((3((-3(-3(5x - 3)^2 - 4(5x - 3) + 2) - 1)/(-2(-3(5x - 3)^2 ... | 0 | MATH |
[
{
"content": "How many local minima does the function f(x) = -3|((3(3(2(1(1x^2 + 1x + 2)^2 - 3)^2 + 2(1(1x^2 + 1x + 2)^2 - 3)) - 1) - 3)/(2(3(2(1(1x^2 + 1x + 2)^2 - 3)^2 + 2(1(1x^2 + 1x + 2)^2 - 3)) - 1)))| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 5((2(4(1(1((-1x)/(1x + 2))^2 - 3((-1x)/(1x + 2)) + 2)^2 - 5(1((-1x)/(1x + 2))^2 - 3((-1x)/(1x + 2)) + 2))^2 + 1(1(1((-1x)/(1x + 2))^2 - 3((-1x)/(1x + 2)) + 2)^2 - 5(1((-1x)/(1x + 2))^2 - 3((-1x)/(1x + 2)) + 2)) - 1) + 3)/... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1|(1|(2(3|(3(2x^2 + 3x + 1)^2 - 4(2x^2 + 3x + 1) - 1) + 1| + 2) - 2) + 1| + 2) + 3| - 2 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 extrema of the function f(x) = (3(-2e^(-1(-1(-3(-1((2x - 3)/(1x + 1)) - 1)^2 + 5(-1((2x - 3)/(1x + 1)) - 1) - 3) - 4)) - 2))/(-3(-2e^(-1(-1(-3(-1((2x - 3)/(1x + 1)) - 1)^2 + 5(-1((2x - 3)/(1x + 1)) - 1) - 3) - 4)) - 2) - 1) in the interval [-10, 10]. ... | 6 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2(1(-3|((1(2(1|x - 2| - 1)^2 - 2(1|x - 2| - 1) + 5))/(-3(2(1|x - 2| - 1)^2 - 2(1|x - 2| - 1) + 5) + 2)) + 2|)^2 + 2(-3|((1(2(1|x - 2| - 1)^2 - 2(1|x - 2| - 1) + 5))/(-3(2(1|x - 2| - 1)^2 - 2(1|x - 2| - 1) + 5) + 2)) + 2|... | 4 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = -1(-1|(-1|(-3cos(1π(2(3x + 2)^2 - 1(3x + 2) + 2)) + 1) + 2| + 1) + 3| - 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 502 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3|(3(1|(1(1(-3x^2 - 1x)^2 - 5)^2 - 5(1(-3x^2 - 1x)^2 - 5) + 4) + 2| - 1) - 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 average of all x-coordinates of local minima of the function f(x) = 2cos(3π(-3((-1(-2|(2(2|x + 1| + 2) - 2) - 3| + 1) + 1)/(2(-2|(2(2|x + 1| + 2) - 2) - 3| + 1) - 1))^2 - 4((-1(-2|(2(2|x + 1| + 2) - 2) - 3| + 1) + 1)/(2(-2|(2(2|x + 1| + 2) - 2) - 3| + 1) - 1)) + 4) - 2) - 2 in the interva... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = (-3(-1e^(1((2(-3((3(2x^2 - 4x + 5) - 2)/(-3(2x^2 - 4x + 5) + 1)) + 1))/(-1(-3((3(2x^2 - 4x + 5) - 2)/(-3(2x^2 - 4x + 5) + 1)) + 1) + 3))) + 2) + 3)/(-3(-1e^(1((2(-3((3(2x^2 - 4x + 5) - 2)/(-3(2x^2 - 4x + 5) + 1)) + 1))/(-1(-3((3(2x... | 1 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2|(-3e^(1(4(-5((-2(-5x^2 + 1x + 2) + 2)/(3(-5x^2 + 1x + 2) - 1))^2 - 5((-2(-5x^2 + 1x + 2) + 2)/(3(-5x^2 + 1x + 2) - 1)) - 1) + 4))) - 1| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer i... | 1 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3(2sin(3π((-2(4(5(1|x - 2| - 3)^2 - 1(1|x - 2| - 3)) - 2) - 2)/(-1(4(5(1|x - 2| - 3)^2 - 1(1|x - 2| - 3)) - 2))) - 1))^2 + 2(2sin(3π((-2(4(5(1|x - 2| - 3)^2 - 1(1|x - 2| - 3)) - 2) - 2)/(-1(4(5(1|x - 2| - 3)^2 - 1(1|x - 2... | 6 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = -3|(3e^(2(-3((1(-3|(-4x^2 + 4x - 4) - 3| + 1) - 2)/(1(-3|(-4x^2 + 4x - 4) - 3| + 1) + 1))^2 - 3((1(-3|(-4x^2 + 4x - 4) - 3| + 1) - 2)/(1(-3|(-4x^2 + 4x - 4) - 3| + 1) + 1))))) - 2| - 2 in the interval [-10, 10]. Round to the neares... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = 3|(-5(2|(-3|(2(-3x^2 + 3x + 1) + 4) - 1|) - 3| - 1)^2 + 1(2|(-3|(2(-3x^2 + 3x + 1) + 4) - 1|) - 3| - 1) - 1) + 3| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | -1 | MATH |
[
{
"content": "How many local minima does the function f(x) = 5((2(2sin(3π((3(-1(-4x^2 + 2x - 5)^2 + 1(-4x^2 + 2x - 5) - 3) - 2)/(3(-1(-4x^2 + 2x - 5)^2 + 1(-4x^2 + 2x - 5) - 3) + 2))) - 1) + 3)/(2(2sin(3π((3(-1(-4x^2 + 2x - 5)^2 + 1(-4x^2 + 2x - 5) - 3) - 2)/(3(-1(-4x^2 + 2x - 5)^2 + 1(-4x^2 + 2x - 5) - 3) + 2)... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2|(-2(2|(2|(-5((2x - 2)/(3x - 2))^2 - 1((2x - 2)/(3x - 2)) + 2) - 2| + 1) - 3| - 2)^2 + 2(2|(2|(-5((2x - 2)/(3x - 2))^2 - 1((2x - 2)/(3x - 2)) + 2) - 2| + 1) - 3| - 2)) + 1| - 2 in the interval [-10, 10]. Round to the nea... | 1 | MATH |
[
{
"content": "How many local minima does the function f(x) = 3((2(2e^(-2(4(-5(-4x^2 - 4x + 4) + 2) + 5)) - 2) - 3)/(2(2e^(-2(4(-5(-4x^2 - 4x + 4) + 2) + 5)) - 2) - 1))^2 - 2((2(2e^(-2(4(-5(-4x^2 - 4x + 4) + 2) + 5)) - 2) - 3)/(2(2e^(-2(4(-5(-4x^2 - 4x + 4) + 2) + 5)) - 2) - 1)) - 5 have in the interval [-10, 10... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 4(-1|(-2((-3(-4((-1x - 2)/(-1x + 2))^2 + 2((-1x - 2)/(-1x + 2))) + 1)/(2(-4((-1x - 2)/(-1x + 2))^2 + 2((-1x - 2)/(-1x + 2))) + 3)) - 5)| + 2) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answe... | 2 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = 3|(-2|(4(-4(-2e^(-1((3x - 1)/(-1x - 3))) + 2)^2 + 2(-2e^(-1((3x - 1)/(-1x - 3))) + 2) - 2)^2 - 2(-4(-2e^(-1((3x - 1)/(-1x - 3))) + 2)^2 + 2(-2e^(-1((3x - 1)/(-1x - 3))) + 2) - 2) + 1) - 1| - 1) + 1| in the interval [-10, 10]. Round ... | -3 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3((1(1(-2(3|(2x^2 - 4x + 2) - 3| - 1)) - 5) + 3)/(-2(1(-2(3|(2x^2 - 4x + 2) - 3| - 1)) - 5) + 3))^2 - 5((1(1(-2(3|(2x^2 - 4x + 2) - 3| - 1)) - 5) + 3)/(-2(1(-2(3|(2x^2 - 4x + 2) - 3| - 1)) - 5) + 3)) - 1 in the interval... | 1 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = (3((1(3(-5(3(-3|x + 3| + 1) + 1) - 5) - 1) - 1)/(-3(3(-5(3(-3|x + 3| + 1) + 1) - 5) - 1) + 1)) + 2)/(2((1(3(-5(3(-3|x + 3| + 1) + 1) - 5) - 1) - 1)/(-3(3(-5(3(-3|x + 3| + 1) + 1) - 5) - 1) + 1))) in the interval [-10, 10]. Round to ... | -3 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1(4(-2|((3(3|(1x + 5) + 1| + 1) - 3)/(1(3|(1x + 5) + 1| + 1) - 3)) + 2| + 3) + 2) - 5 have in the interval [-10, 10]?\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) = 1(2|(-2((-2((3((-3x - 2)/(1x - 2)) + 3)/(2((-3x - 2)/(1x - 2)) + 3)) - 1)/(-2((3((-3x - 2)/(1x - 2)) + 3)/(2((-3x - 2)/(1x - 2)) + 3)) + 1))^2 + 4((-2((3((-3x - 2)/(1x - 2)) + 3)/(2((-3x - 2)/(1x - 2)) + 3)) - 1)/(-2((3((-3x ... | 6 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = (2(-3(-1(-1(-3|((-1x + 2)/(1x)) + 3| - 3)^2 + 2(-3|((-1x + 2)/(1x)) + 3| - 3)) - 4)^2 - 4(-1(-1(-3|((-1x + 2)/(1x)) + 3| - 3)^2 + 2(-3|((-1x + 2)/(1x)) + 3| - 3)) - 4) - 3) + 1)/(1(-3(-1(-1(-3|((-1x + 2)/(1x)) + 3| - 3)^2 + 2(-3|((-... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -2sin(2π(1((1(2|(1(1x^2 - 5x - 1)^2 + 1(1x^2 - 5x - 1) - 4) - 1| - 2) + 1)/(-2(2|(1(1x^2 - 5x - 1)^2 + 1(1x^2 - 5x - 1) - 4) - 1| - 2) + 3)) - 3) - 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent... | 6 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1(-3(2(4((-2(3sin(1πx - 1) - 1) + 2)/(2(3sin(1πx - 1) - 1)))^2 + 4((-2(3sin(1πx - 1) - 1) + 2)/(2(3sin(1πx - 1) - 1))) - 2) - 4)^2 - 1(2(4((-2(3sin(1πx - 1) - 1) + 2)/(2(3sin(1πx - 1) - 1)))^2 + 4((-2(3sin(1... | -9 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = -1(5(2e^(1(-4(3|(2|x + 2|) + 1| + 3) + 1)) - 2)^2 - 1(2e^(1(-4(3|(2|x + 2|) + 1| + 3) + 1)) - 2) - 2)^2 + 5(5(2e^(1(-4(3|(2|x + 2|) + 1| + 3) + 1)) - 2)^2 - 1(2e^(1(-4(3|(2|x + 2|) + 1| + 3) + 1)) - 2) - 2) - 3 in the interval [-10... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (1((1((-3(1(2sin(3π(4x + 5)) + 3) - 4) - 3)/(-1(1(2sin(3π(4x + 5)) + 3) - 4) - 2)) + 2)/(1((-3(1(2sin(3π(4x + 5)) + 3) - 4) - 3)/(-1(1(2sin(3π(4x + 5)) + 3) - 4) - 2)) + 1)) + 2)/(1((1((-3(1(2sin(3π(4x + 5))... | -10 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = (1(3|(-1|((3((-1(2x - 4))/(-3(2x - 4) - 3)) + 2)/(-2((-1(2x - 4))/(-3(2x - 4) - 3)) - 1)) + 1|) + 2| + 1))/(-3(3|(-1|((3((-1(2x - 4))/(-3(2x - 4) - 3)) + 2)/(-2((-1(2x - 4))/(-3(2x - 4) - 3)) - 1)) + 1|) + 2| + 1)) have in th... | 253 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-3(3|((-1((-2(2((-2x + 2)/(1x - 2))^2 + 4((-2x + 2)/(1x - 2)) + 1) + 2)/(-2(2((-2x + 2)/(1x - 2))^2 + 4((-2x + 2)/(1x - 2)) + 1) - 2)) + 3)/(2((-2(2((-2x + 2)/(1x - 2))^2 + 4((-2x + 2)/(1x - 2)) + 1) + 2)/(... | 0 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (-2((2(2e^(-1((2(2|(-3|x + 2| - 1) + 2| + 1) + 1)/(-2(2|(-3|x + 2| - 1) + 2| + 1) + 1)))) + 1)/(2(2e^(-1((2(2|(-3|x + 2| - 1) + 2| + 1) + 1)/(-2(2|(-3|x + 2| - 1) + 2| + 1) + 1)))) + 2)) + 1)/(-2((2(2e^(-1((2(2|(-3|x + 2| - 1) + 2| + 1) + 1)/(-2(2|(-3... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = -2cos(1π((2(3|(4(-2(-2|x - 3| + 3) - 2)) - 2| + 1))/(-2(3|(4(-2(-2|x - 3| + 3) - 2)) - 2| + 1) + 1)) + 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -3|(2|(3(3|(-2|(2e^(1x)) - 2| + 3) + 3|)^2 - 1(3|(-2|(2e^(1x)) - 2| + 3) + 3|)) + 1| + 1) - 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 0 | MATH |
[
{
"content": "How many local minima does the function f(x) = (2((3(-3(-1|((1((-2x)/(3x - 2)) - 1)/(3((-2x)/(3x - 2)) - 1)) - 1| + 1) + 4))/(3(-3(-1|((1((-2x)/(3x - 2)) - 1)/(3((-2x)/(3x - 2)) - 1)) - 1| + 1) + 4) - 1)) + 3)/(-3((3(-3(-1|((1((-2x)/(3x - 2)) - 1)/(3((-2x)/(3x - 2)) - 1)) - 1| + 1) + 4))/(3(-3(-1|... | 0 | MATH |
[
{
"content": "How many local minima does the function f(x) = 2|((-1(-4((-1(2|(-3|x| - 2) + 2| + 2) - 2)/(3(2|(-3|x| - 2) + 2| + 2) - 1)) + 5) - 1)/(-3(-4((-1(2|(-3|x| - 2) + 2| + 2) - 2)/(3(2|(-3|x| - 2) + 2| + 2) - 1)) + 5) - 1)) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1(-3|(5(4(2((2x - 3)/(-3x - 2))^2 - 4((2x - 3)/(-3x - 2)) - 3)^2 - 2(2((2x - 3)/(-3x - 2))^2 - 4((2x - 3)/(-3x - 2)) - 3) + 3) + 2) + 3| + 2)^2 + 1(-3|(5(4(2((2x - 3)/(-3x - 2))^2 - 4((2x - 3)/(-3x - 2)) - 3)^2 - 2(2((2x -... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2cos(1π((-1(2|((1(2|((-1x - 2)/(-1x + 2)) + 2| - 3) + 1)/(-3(2|((-1x - 2)/(-1x + 2)) + 2| - 3) + 1)) + 2|) + 2)/(-2(2|((1(2|((-1x - 2)/(-1x + 2)) + 2| - 3) + 1)/(-3(2|((-1x - 2)/(-1x + 2)) + 2| - 3) + 1)) ... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1sin(3π(4(-4(-1(-3((-1x)/(-1x + 3)) - 2) + 5)^2 - 2(-1(-3((-1x)/(-1x + 3)) - 2) + 5) + 3)^2 + 4(-4(-1(-3((-1x)/(-1x + 3)) - 2) + 5)^2 - 2(-1(-3((-1x)/(-1x + 3)) - 2) + 5) + 3) + 4) - 3) + 3 in the interval... | -9 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 3|((-1(-2|(-4(-2(-1e^(-2x) + 3)^2 + 2(-1e^(-2x) + 3) + 1) - 2) - 1| - 3) - 1)/(-2(-2|(-4(-2(-1e^(-2x) + 3)^2 + 2(-1e^(-2x) + 3) + 1) - 2) - 1| - 3))) - 3| + 1 in the interval [-10, 10]. Round to the nearest ... | 10 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1cos(1π(1|((2((2((-3(-2x - 5) + 3)/(1(-2x - 5) + 2)) + 1)/(3((-3(-2x - 5) + 3)/(1(-2x - 5) + 2)))) - 3)/(2((2((-3(-2x - 5) + 3)/(1(-2x - 5) + 2)) + 1)/(3((-3(-2x - 5) + 3)/(1(-2x - 5) + 2)))) + 1)) - 1| - 2) - 1) - 3 in ... | -3 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2cos(3π(-4(-3((1(-1(-1x^2 + 5x + 1)^2 - 4(-1x^2 + 5x + 1) - 2) - 2)/(2(-1(-1x^2 + 5x + 1)^2 - 4(-1x^2 + 5x + 1) - 2) - 3)) - 1) - 5)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent... | 2 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = -2e^(-2(1(-1(-3(1((-3x + 1)/(1x - 3)) + 5)^2 - 2(1((-3x + 1)/(1x - 3)) + 5) - 1)^2 + 1)^2 + 2(-1(-3(1((-3x + 1)/(1x - 3)) + 5)^2 - 2(1((-3x + 1)/(1x - 3)) + 5) - 1)^2 + 1) - 1)) - 2 in the interval [-10, 10]. Round to the... | 7 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 2sin(3π((3(-3|((-1((-1(1x^2 - 4x + 3) + 3)/(-2(1x^2 - 4x + 3))))/(-1((-1(1x^2 - 4x + 3) + 3)/(-2(1x^2 - 4x + 3))) + 3)) + 3| - 2) + 2)/(-1(-3|((-1((-1(1x^2 - 4x + 3) + 3)/(-2(1x^2 - 4x + 3))))/(-1((-1(1x^2 -... | 1 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 3|(-3|(-4(-1|(-2sin(1π((2x - 1)/(-1x + 3))) + 3) + 3|)^2 - 3(-1|(-2sin(1π((2x - 1)/(-1x + 3))) + 3) + 3|) - 4) + 3| + 3) + 2| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answ... | -7 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 3|((-3(-1((-3(2(-4x^2 - 2x + 5) - 3) + 3)/(3(2(-4x^2 - 2x + 5) - 3) + 3))^2 - 5((-3(2(-4x^2 - 2x + 5) - 3) + 3)/(3(2(-4x^2 - 2x + 5) - 3) + 3)) + 2) - 2)/(1(-1((-3(2(-4x^2 - 2x + 5) - 3) + 3)/(3(2(-4x^2 - 2x + 5) - 3) + 3))... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = 4(3(1((3(3(1x^2 - 2x + 5)^2 - 2(1x^2 - 2x + 5) + 5) + 1)/(3(3(1x^2 - 2x + 5)^2 - 2(1x^2 - 2x + 5) + 5) - 2))^2 + 2)^2 + 2(1((3(3(1x^2 - 2x + 5)^2 - 2(1x^2 - 2x + 5) + 5) + 1)/(3(3(1x^2 - 2x + 5)^2 - 2(1x^2 - 2x + 5) + 5) - 2))^2 + 2... | 1 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-3((-2(2(1sin(1π(-1((-2x + 1)/(-1x + 3))^2 + 4) + 1) - 2)^2 + 3(1sin(1π(-1((-2x + 1)/(-1x + 3))^2 + 4) + 1) - 2) - 1))/(-3(2(1sin(1π(-1((-2x + 1)/(-1x + 3))^2 + 4) + 1) - 2)^2 + 3(1sin(1π(-1((-2x + 1)/(-1x + 3))^2 + 4) +... | 4 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = (2(-1|(3|((2(-3|(-3x^2 - 5) + 2| + 1) - 2)/(3(-3|(-3x^2 - 5) + 2| + 1) - 2)) - 1| + 3) + 3| - 1) + 2)/(-2(-1|(3|((2(-3|(-3x^2 - 5) + 2| + 1) - 2)/(3(-3|(-3x^2 - 5) + 2| + 1) - 2)) - 1| + 3) + 3| - 1) - 1) in the interval [-10, 10]. ... | 0 | MATH |
[
{
"content": "How many local minima does the function f(x) = 5(2((1(-2|(2|(-4x^2 - 5x - 5) - 2|)|) + 1)/(-2(-2|(2|(-4x^2 - 5x - 5) - 2|)|) + 3)) + 4) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
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