What is the extreme f(x)=5sin^2(x) ?

The extreme f(x)=5sin^2(x) is Minimum(pin,0),Maximum(pi/2+pin,5)

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extreme f(x)=5sin^2(x)

extreme

Minimum (πn, 0), Maximum (\frac{π}{2} + πn, 5)

Solution steps

Find the critical points:

x = πn, x = \frac{π}{2} + πn

Domain of

5 sin^{2} (x) : - \infty < x < \infty

Find intervals:

Increasing

: πn < x < \frac{π}{2} + πn,

Decreasing

: \frac{π}{2} + πn < x < π + πn

Plug the extreme point

x = πn

into

5 sin^{2} (x) \Rightarrow y = 0

Minimum (πn, 0)

Plug the extreme point

x = \frac{π}{2} + πn

into

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

Maximum (\frac{π}{2} + πn, 5)

Minimum (πn, 0), Maximum (\frac{π}{2} + πn, 5)

What is the extreme f(x)=5sin^2(x) ?
The extreme f(x)=5sin^2(x) is Minimum(pin,0),Maximum(pi/2+pin,5)