Answer
$7$
Work Step by Step
General formula for average rate of change from $a$ to $b$: $\frac{f(b)-f(a)}{b-a}.$
Hence here: $\frac{f(3)-f(1)}{3-1}=\frac{(3\cdot3^2-5\cdot3)-(3\cdot1^2-5\cdot1)}{2}=\frac{(27-15)-(3-5)}{2}=\frac{(12-(-2))}{2}=\frac{14}{2}=7.$
