What is the extreme f(x)=5sin(x)cos(x),(-pi,pi) ?

The extreme f(x)=5sin(x)cos(x),(-pi,pi) is

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extreme f(x)=5sin(x)cos(x),(-pi,pi)

extreme points

f (x) = 5 sin (x) cos (x), (- π, π)

Maximum (- \frac{3 π}{4}, \frac{5}{2}), Minimum (- \frac{π}{4}, - \frac{5}{2}), Maximum (\frac{π}{4}, \frac{5}{2}), Minimum (\frac{3 π}{4}, - \frac{5}{2})

Solution steps

Find the critical points:

x = - \frac{3 π}{4}, x = - \frac{π}{4}, x = \frac{π}{4}, x = \frac{3 π}{4}

Domain of

5 sin (x) cos (x), (- π, π) : - π < x < π

Find intervals:

Increasing

: - π < x < - \frac{3 π}{4},

Decreasing

: - \frac{3 π}{4} < x < - \frac{π}{4},

Increasing

: - \frac{π}{4} < x < \frac{π}{4},

Decreasing

: \frac{π}{4} < x < \frac{3 π}{4},

Increasing

: \frac{3 π}{4} < x < π

Plug the extreme point

x = - \frac{3 π}{4}

into

5 sin (x) cos (x) \Rightarrow y = \frac{5}{2}

Maximum (- \frac{3 π}{4}, \frac{5}{2})

Plug the extreme point

x = - \frac{π}{4}

into

5 sin (x) cos (x) \Rightarrow y = - \frac{5}{2}

Minimum (- \frac{π}{4}, - \frac{5}{2})

Plug the extreme point

x = \frac{π}{4}

into

5 sin (x) cos (x) \Rightarrow y = \frac{5}{2}

Maximum (\frac{π}{4}, \frac{5}{2})

Plug the extreme point

x = \frac{3 π}{4}

into

5 sin (x) cos (x) \Rightarrow y = - \frac{5}{2}

Minimum (\frac{3 π}{4}, - \frac{5}{2})

Maximum (- \frac{3 π}{4}, \frac{5}{2}), Minimum (- \frac{π}{4}, - \frac{5}{2}), Maximum (\frac{π}{4}, \frac{5}{2}), Minimum (\frac{3 π}{4}, - \frac{5}{2})

y = j + x

f (x, y) = 2 x^{2} + y^{2} - 2 x y + 5 x - 3 y + 1

f (x) = \frac{x ^{2} + 2}{x ^{2} - 4 x}

f (x) = x^{5} - 10 x^{4}

f (x) = x^{7} ln (x)

What is the extreme f(x)=5sin(x)cos(x),(-pi,pi) ?
The extreme f(x)=5sin(x)cos(x),(-pi,pi) is