Chapter 4.2, Problem 23E

  Mean Value Theorem Consider the following functions on the given interval [a, b].

  a.    Determine whether the Mean Value Theorem applies to the following functions on the given interval [a, b].

  b.    If so, find the point(s) that are guaranteed to exist by the Mean Value Theorem.

23.     $f\left(x\right)=\{\begin{array}{ll}-2x\hfill & \text{if }x<0\hfill \\ x\hfill & \text{if }x\ge 0\hfill \end{array};\left[-1,\text{ 1}\right]$