Question

The number of values of $x\in [0,2]$ at which $f\left(x\right)=|x-\frac{1}{2}|+|x-1|+\tan x$ is not differentiable is/are

• A. $0$
• B. $1$
• C. $3$
• D. None of the above

Answer 1

The correct option is C $3$

$|x-\frac{1}{2}|$ is continuous everywhere but not differentiable at $x=\frac{1}{2},|x-1|$ is continuous everywhere but not differentiable at x$=1$, and $tanx$ is continuous in [0, 2] except at $x=\frac{\pi }{2}$.Therefore, f(x) is not differentiable at $x=\frac{1}{2},1,\frac{\pi }{2}$.
Hence, option 'C' is correct.