Answer
$f'(0)=0$ and $f'(2)=0.$
Work Step by Step
Using the chain rule with $u=\frac{\pi}{2}x\to \dfrac{du}{dx}=\frac{\pi}{2}.$
$f'(x)=-\sin{\frac{\pi x}{2}}\times\frac{\pi}{2}=-\frac{\pi}{2}\sin{\frac{\pi x}{2}}.$
$f'(0)=-\frac{\pi}{2}\sin{\frac{\pi(0)}{2}}=0.$
$f'(2)=-\frac{\pi}{2}\sin{\frac{\pi (2)}{2}}=0.$
