Question

In $(0,2\pi )$ , the total number of points, where $f\left(x\right)=max\left\{sinx,cosx,1-cosx\right\}$ is not differentiable, is

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

Answer: (A)

$f\left(x\right)=max\left\{sinx,cosx,1-cosx\right\}$
The graph of $f\left(x\right)$ is

$\Rightarrow$ $f\left(x\right)$ is not differentiable at sharp points, which are $x=\frac{\pi }{4},\frac{\pi }{2},\frac{5\pi }{3}$ .
$\Rightarrow$ $f\left(x\right)$ is not differentiable at $3$ points.