Chapter 4, Problem 76RE

In each part, determine whether all of the hypotheses of the Mean-Value Theorem are satisfied on the stated interval. If not, state which hypotheses fail; if so, find all values of $c$ guaranteed in the conclusion of the theorem.

(a) $f\left(x\right)=\left|x-1\right|\text{ on }\left[-2,2\right]$

(b) $f\left(x\right)=\frac{x+1}{x-1}\text{ on }\left[2,3\right]$

(c) $f\left(x\right)=\left\{\begin{array}{cc}3-x^2& \text{if }x\le 1\\ 2/x& \text{if }x>1\end{array}\right.\text{ on }\left[0,2\right]$