Answer is $(d)$
$f '(s) = \cos x =0$ gives root $\frac{\pi}{2}$ and $\frac{3\pi}{2}$ which lie between the given domain in question $\left[\frac{\pi}{4},\frac{7\pi}{4}\right]$
$f ''(x)= - \sin x$ at $\frac{\pi}{2}$ gives $-1<0$ which means it is local maxima and at $\frac{3\pi}{2}$ it gives $1>0$ which is local minima.
Since, at $\frac{\pi}{2}$ it is local maxima so, before it, graph is strictly increasing, so $\frac{\pi}{4}$ is also local minima.
So, there are two local minima $\frac{\pi}{4}$ and $\frac{3\pi}{2}.$