Define \(f: \mathbb{R} \rightarrow \mathbb{R}\) by \[f(x)= \begin{cases}(1-\cos x) \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{cases}\] Then,\(\qquad\) (a) \(f\) is discontinuous. \(\qquad\) (b) \(f\) is continuous but not differentiable. \(\qquad\) \(\qquad\) \(\qquad\) (c) \(f\) is differentiable and its derivative is discontinuous. \(\qquad\) \(\qquad\) \(\qquad\)\(\qquad\)\(\qquad\) \(\qquad\) (d) \(f\) is differentiable and its derivative is continuous.