JEE Math Practice Question

Let $$f(x) = \left\{ {\begin{matrix} {{x^2}\sin \left( {{1 \over x}} \right)} & {,\,x \ne 0} \\ 0 & {,\,x = 0} \\ \end{matrix} } \right.$$ Then at $$x=0$$

1. A.$$f$$ is continuous but $$f'$$ is not continuous
2. B.$$f$$ and $$f'$$ both are continuous
3. C.$$f$$ is continuous but not differentiable
4. D.$$f'$$ is continuous but not differentiable