Mathematics - Application of Derivative Question with Solution | TestHub

$\frac{dy}{dx}=\frac{1-\cos x}{2\sqrt{x+\sin x}}=0\Rightarrow \cos x=1\Rightarrow x=0,\pm 2\pi ,\pm 4\pi \dots$. $\therefore x\in [-10,10]\Rightarrow x=0,\pm 2\pi$

For $x=0,y=0$. $\begin{array}{l}x=0,y=0\\ x=2\pi ,y=\pm \sqrt{2}\pi \end{array}\}$ they satisfy $-3\le y\le 3$. $x=-2\pi ,y^2=-2\pi$.

Also, the slope at $(0,0)$ is undefined, hence points are $(2\pi ,2\pi )$ and $(2\pi ,-\sqrt{2\pi })$.