What is the extreme f(x)=sin(pix) ?

The extreme f(x)=sin(pix) is Maximum(1/2+2n,1),Minimum(3/2+2n,-1)

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extreme f(x)=sin(pix)

extreme points

f (x) = sin (π x)

Maximum (\frac{1}{2} + 2 n, 1), Minimum (\frac{3}{2} + 2 n, - 1)

Solution steps

Find the critical points:

x = \frac{1}{2} + 2 n, x = \frac{3}{2} + 2 n

Domain of

sin (π x) : - \infty < x < \infty

Find intervals:

Increasing

: 2 n \leq x < \frac{1}{2} + 2 n,

Decreasing

: \frac{1}{2} + 2 n < x < \frac{3}{2} + 2 n,

Increasing

: \frac{3}{2} + 2 n < x < 2 + 2 n

Plug the extreme point

x = \frac{1}{2} + 2 n

into

sin (π x) \Rightarrow y = 1

Maximum (\frac{1}{2} + 2 n, 1)

Plug the extreme point

x = \frac{3}{2} + 2 n

into

sin (π x) \Rightarrow y = - 1

Minimum (\frac{3}{2} + 2 n, - 1)

Maximum (\frac{1}{2} + 2 n, 1), Minimum (\frac{3}{2} + 2 n, - 1)

What is the extreme f(x)=sin(pix) ?
The extreme f(x)=sin(pix) is Maximum(1/2+2n,1),Minimum(3/2+2n,-1)