What is the extreme f(x)=cos(pix),0<= x<= 2/3 ?

The extreme f(x)=cos(pix),0<= x<= 2/3 is Maximum(0,1),Minimum(2/3 ,-1/2)

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extreme f(x)=cos(pix),0<= x<= 2/3

extreme

Maximum (0, 1), Minimum (\frac{2}{3}, - \frac{1}{2})

Solution steps

Find the critical points:

x = 0, x = \frac{2}{3}

Domain of

cos (π x), 0 \leq x \leq \frac{2}{3} : 0 \leq x \leq \frac{2}{3}

Find intervals:

Decreasing

: 0 < x < \frac{2}{3}

Plug the extreme point

x = 0

into

cos (π x) \Rightarrow y = 1

Maximum (0, 1)

Plug the extreme point

x = \frac{2}{3}

into

cos (π x) \Rightarrow y = - \frac{1}{2}

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

Maximum (0, 1), Minimum (\frac{2}{3}, - \frac{1}{2})

What is the extreme f(x)=cos(pix),0<= x<= 2/3 ?
The extreme f(x)=cos(pix),0<= x<= 2/3 is Maximum(0,1),Minimum(2/3 ,-1/2)