question_answer

If \[f(x)=\left\{ \begin{align}   & \underline{\left| x \right|},x\ne 0 \\  & 0,\,\,\,\,\,x=0 \\ \end{align} \right.\], where f(x) is signum function then the function is:

A)  continuous as well differentiable at \[x=0\]

B)  continuous but not differentiable at \[x=0\]

C)  neither differentiable nor continuous at \[x=0\]

D)  differentiable but continuous at \[x=0\]