Question

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

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

Answer 1

Answer: (D)

The graph of $y=|2 \sin x|$ is given below:

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