What is the extreme f(x)=cos((4x)/3) ?

The extreme f(x)=cos((4x)/3) is Maximum((3pi)/2 n,1),Minimum((3pi)/4+(3pi)/2 n,-1)

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extreme f(x)=cos((4x)/3)

extreme

Maximum (\frac{3 π}{2} n, 1), Minimum (\frac{3 π}{4} + \frac{3 π}{2} n, - 1)

Solution steps

Find the critical points:

x = \frac{3 π}{2} n, x = \frac{3 π}{4} + \frac{3 π}{2} n

Domain of

cos (\frac{4 x}{3}) : - \infty < x < \infty

Find intervals:

Decreasing

: \frac{3 π}{2} n < x < \frac{3 π}{4} + \frac{3 π}{2} n,

Increasing

: \frac{3 π}{4} + \frac{3 π}{2} n < x < \frac{3 π}{2} + \frac{3 π}{2} n

Plug the extreme point

x = \frac{3 π}{2} n

into

cos (\frac{4 x}{3}) \Rightarrow y = 1

Maximum (\frac{3 π}{2} n, 1)

Plug the extreme point

x = \frac{3 π}{4} + \frac{3 π}{2} n

into

cos (\frac{4 x}{3}) \Rightarrow y = - 1

Minimum (\frac{3 π}{4} + \frac{3 π}{2} n, - 1)

Maximum (\frac{3 π}{2} n, 1), Minimum (\frac{3 π}{4} + \frac{3 π}{2} n, - 1)

What is the extreme f(x)=cos((4x)/3) ?
The extreme f(x)=cos((4x)/3) is Maximum((3pi)/2 n,1),Minimum((3pi)/4+(3pi)/2 n,-1)