Question

Find the intervals in which the function $f$ given by $f\left(x\right)=\sin x+\cos x,0\le x\le 2\pi$ is strictly increasing or strictly decreasing

Answer 1

Given,

$f\left(x\right)=\sin x+\cos x$

Differentiating w.r.t. $x$, we get

$f^{\prime }\left(x\right)=\cos x-\sin x$

For critical points $f^{\prime }\left(x\right)=0$