Chapter 2.2, Problem 39ES

The function $f$ whose graph is shown below has values as given in the accompanying table.

(a) Use data from the table to calculate the difference quotients

$\frac{f\left(3\right)-f\left(1\right)}{3-1},\frac{f\left(2\right)-f\left(1\right)}{2-1},\frac{f\left(2\right)-f\left(0\right)}{2-0}$

(b) Using the graph of $y=f\left(x\right)$ , indicate which difference quotient in part (a) best approximates $f^{\prime }\left(1\right)$ and which difference quotient gives the worst approximation to $f^{\prime }\left(1\right)$ .