Answer
19
Work Step by Step
We find the average rate of change of $f(x)$ from 3 to 4:
$\displaystyle \frac{\Delta y}{\Delta x}=\frac{f(4)-f(3)}{4-3}$
$\displaystyle =\frac{[3(4)^{2}-2(4)+4]-[3(3)^{2}-2(3)+4]}{4-3}$
$\displaystyle =\frac{44-25}{4-3}$
$\displaystyle =\frac{19}{1}$
$=19$
