The function y = a(1 - cos x) is maximum when | vedclass

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(A) Given the function $y = a(1 - \cos x)$.First,find the derivative $y'$ with respect to $x$:$y' = \frac{d}{dx}[a(1 - \cos x)] = a(0 - (-\sin x)) = a

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$\pi $

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(A) Given the function $y = a(1 - \cos x)$.First,find the derivative $y'$ with respect to $x$:$y' = \frac{d}{dx}[a(1 - \cos x)] = a(0 - (-\sin x)) = a \sin x$.To find the critical points,set $y' = 0$:$a \sin x = 0 \Rightarrow \sin x = 0 \Rightarrow x = n\pi$ for any integer $n$.Within the standard interval $[0, 2\pi]$,the critical points are $x = 0$ and $x = \pi$.Now,find the second derivative $y''$:$y'' = \frac{d}{dx}(a \sin x) = a \cos x$.Evaluate $y''$ at the critical points:For $x = 0$,$y''(0) = a \cos(0) = a$.For $x = \pi$,$y''(\pi) = a \cos(\pi) = -a$.Assuming $a > 0$,the function has a local maximum when $y'' < 0$,which occurs at $x = \pi$.

The function $y = a(1 - \cos x)$ is maximum when $x = $

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