題組內容

一、Calculus (50% in total)
1. Let $f(x) = \begin{cases} x^3 \sin \frac{1}{x}, & x \neq 0 \\ 0, & x = 0 \end{cases}$.

(b) \( (7\%) \) Prove that \( f(x) \) is differentiable at 0 and find \( f^{\prime}(0) \).