Answer
$19.$
Work Step by Step
General formula for average rate of change from $a$ to $b$: $\frac{f(b)-f(a)}{b-a}.$
Hence here: $\frac{f(4)-f(3)}{4-3}=\frac{(3\cdot4^2-2\cdot4+4)-(3\cdot3^2-2\cdot3+4)}{1}=\frac{(48-8+4)-(27-6+4)}{1}=\frac{(44)-(25)}{1}=19.$
