Question

The function $y=\left|2\sin x\right|$ is continuous for any $x$ but it is not differentiable at

• A. Only $x=0$
• B. Only $x=\pi$
• C. Only $x=\frac{\pi }{2}$
• D. $x=k\pi$ ($k$ is an integer)

Answer 1

The correct option is D $x=k\pi$ ($k$ is an integer)

The graph of $y=\left|2\sin x\right|$ is given below:
It can be easily seen from the graph of $f\left(x\right)=\left|2\sin x\right|$, it is continuous everywhere but not differentiable at integer multiples of $\pi$.