Let $f(x) = |x|\sin x + |x - \pi|\cos x$ for $x \in \mathbb{R}$. Then\\
(a) $f$ is differentiable at $x = 0$ and $x = \pi$\\
(b) $f$ is not differentiable at $x = 0$ and $x = \pi$\\
(c) $f$ is differentiable at $x = 0$ but not differentiable at $x = \pi$\\
(d) $f$ is not differentiable at $x = 0$ but differentiable at $x = \pi$