If $f(x) = [x], x \in \mathbb{R}$ is the greatest integer function, then the correct statement is : (A) $f$ is continuous but not differentiable at $x = 2$. (B) $f$ is neither continuous nor differentiable at $x = 2$. (C) $f$ is continuous as well as differentiable at $x = 2$. (D) $f$ is not continuous but differentiable at $x = 2$.