Chapter 4.2, Problem 5E

For each function f and interval [a, b], a graph of f is given along with the secant line that passes though the graph of f at x = a and x = b.

a.    Use the graph to make a conjecture about the value(s) of c satisfying the equation $\frac{f\left(b\right)-f\left(a\right)}{b-a}=f^{\prime }\left(c\right).$

b.    Verify your answer to part (a) by solving the equation $\frac{f\left(b\right)-f\left(a\right)}{b-a}=f^{\prime }\left(c\right)$ for c.

5.     $f\left(x\right)=\frac{x^2}{4}+1;\left[-2,4\right]$