Let $$f(x) = \begin{cases} (x - 1)\sin\left(\frac{1}{x - 1}\right), & \text{if } x \ne 1 \\ 0, & \text{if } x = 1 \end{cases}$$. Then which one of the following is true?

A

f is neither differentiable at $$x = 0$$ nor at $$x = 1$$

B

f is differentiable at $$x = 0$$ and at $$x = 1$$

C

f is differentiable at $$x = 0$$ but not at $$x = 1$$

D

f is differentiable at $$x = 1$$ but not at $$x = 0$$