(b) Proof that If $f \to \mathbb{R}$ is differentiable at $x = c$, then $f$ is continuous at $c$.
(c) Use the Mean Value Theorem to show that if $0 < x < \frac{\pi}{3}$, then $-\frac{1}{2}x \le \sin x \le x$.
(d) Let $f(x) = 1 - x^3$.
Show that $f(1) = f(-1) = 0$, but that $f'(x)$ is never zero in the interval $[-1, 1]$.
Explain how this is possible in respect to Rolle's theorem.
