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

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

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extreme f(x)=cos(pix)

extreme

Maximum (2 n, 1), Minimum (1 + 2 n, - 1)

Solution steps

Find the critical points:

x = 2 n, x = 1 + 2 n

Domain of

cos (π x) : - \infty < x < \infty

Find intervals:

Decreasing

: 2 n < x < 1 + 2 n,

Increasing

: 1 + 2 n < x < 2 + 2 n

Plug the extreme point

x = 2 n

into

cos (π x) \Rightarrow y = 1

Maximum (2 n, 1)

Plug the extreme point

x = 1 + 2 n

into

cos (π x) \Rightarrow y = - 1

Minimum (1 + 2 n, - 1)

Maximum (2 n, 1), Minimum (1 + 2 n, - 1)

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