What is the extreme f(x)=sin^2(13x) ?

The extreme f(x)=sin^2(13x) is Minimum(pi/(13)n,0),Maximum(pi/(26)+pi/(13)n,1)

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extreme f(x)=sin^2(13x)

extreme points

f (x) = sin^{2} (13 x)

Minimum (\frac{π}{13} n, 0), Maximum (\frac{π}{26} + \frac{π}{13} n, 1)

Solution steps

Find the critical points:

x = \frac{π}{13} n, x = \frac{π}{26} + \frac{π}{13} n

Domain of

sin^{2} (13 x) : - \infty < x < \infty

Find intervals:

Increasing

: \frac{π}{13} n < x < \frac{π}{26} + \frac{π}{13} n,

Decreasing

: \frac{π}{26} + \frac{π}{13} n < x < \frac{π}{13} + \frac{π}{13} n

Plug the extreme point

x = \frac{π}{13} n

into

sin^{2} (13 x) \Rightarrow y = 0

Minimum (\frac{π}{13} n, 0)

Plug the extreme point

x = \frac{π}{26} + \frac{π}{13} n

into

sin^{2} (13 x) \Rightarrow y = 1

Maximum (\frac{π}{26} + \frac{π}{13} n, 1)

Minimum (\frac{π}{13} n, 0), Maximum (\frac{π}{26} + \frac{π}{13} n, 1)

What is the extreme f(x)=sin^2(13x) ?
The extreme f(x)=sin^2(13x) is Minimum(pi/(13)n,0),Maximum(pi/(26)+pi/(13)n,1)