If the solve the problem


$f(x)=\cos x, 0


Given : $f(x)=\cos x$

$\Rightarrow f^{\prime}(x)=-\sin x$

For a local maximum or a local minimum, we must have


$\Rightarrow-\sin x=0$

$\Rightarrow \sin x=0$

$\Rightarrow x=0$ or $\pi$

Since $0

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