Question

The critical point(s) of $f\left(x\right)=max\{\sin x,\cos x\}\forall x\in (0,2\pi )$ is/are:

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{2}$
• C. $\frac{3\pi }{2}$
• D. $\frac{5\pi }{4}$

Answer 1

Answer: (A), (B), (D)

$\frac{5\pi }{4}$

Given $f\left(x\right)=max\{\sin x,\cos x\}$
The possible figure of $f\left(x\right)$ is:
from figure it is clear that $f\left(x\right)$ has three critical points $x=\{\frac{\pi }{4},\frac{\pi }{2},\frac{5\pi }{4}\}$