JEE Math Practice Question

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

1. A.$$f$$ is neither differentiable at x = 0 nor at x = 1
2. B.$$f$$ is differentiable at x = 0 and at x = 1
3. C.$$f$$ is differentiable at x = 0 but not at x = 1
4. D.$$f$$ is differentiable at x = 1 but not at x = 0