Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be a function defined as $f(x)=|x|$. Then $f$ is

Continuous and differentiable at 0 Neither continuous nor differentiable at 0 Continuous but not differentiable at 0 None of the above

Continuous but not differentiable at 0

$f$ is continuous at the point 0 because $\lim_{x \to 0}f(x)=0=f(0)$ whereas $\lim_{h \to 0+}{f(0+h)-f(0)}/h=1$ and $\lim_{h \to 0-}{f(0+h)-f(0)/h}=-1$, hence $f$ is not differentiable at 0.