Question

If $f(x)=\begin{cases}\frac{x}{|x|}when~x\ne0\\ |x|when~x=0\end{cases}$ is a real valued function, then}

• A. f is continuous but not differentiable at $x=0$
• B. f is both continuous and differentiable at $x=0$
• C. f is not defined at $x=0$
• D. f is neither continuous nor differentiable at $x=0$ \bigskip

Hint:

Discontinuity automatically implies non-differentiability.

Answer 1

The Correct Option is D