Consider the function $f : \mathbb{R} \longrightarrow \mathbb{R}$, defined as follows:
$$f(x) = \begin{cases} (x-1)\min\left\{x, x^2\right\} & \text{if } x \geq 0 \\ x\min\left\{x, \frac{1}{x}\right\} & \text{if } x < 0 \end{cases}$$
Then, $f$ is\\
(A) differentiable everywhere.\\
(B) not differentiable at exactly one point.\\
(C) not differentiable at exactly two points.\\
(D) not differentiable at exactly three points.