Chapter 4.8, Problem 15ES

Let $f\left(x\right)=\tan x$ .

(a) Show that there is no point $c$ in the interval $\left(0,\pi \right)$ such that $f^{\prime }\left(c\right)=0,$ even though $f\left(0\right)=f\left(\pi \right)=0$ .

(b) Explain why the result in part (a) does not contradict Rolle’s Theorem.