Answer
$7$
Work Step by Step
Average rate of change from $a$ to $b$: $=\dfrac{f(b)-f(a)}{b-a}$
Wth $a=1$ and $b=3$:
$\begin{aligned} f(b)=f(3) &=3(3)^{2}-5(3) \\ &=3(9)-15 \\ &=27 - 15 \\ &=12 \\
\\f(a)=f(1) &=3(1)^{2}-5(1) \\ &=3-5 \\ &=-2\\
\\\text{substituting these values in the rate of change formula above yields}\\
\\&=\frac{12-(-2)}{3-1} \\
\\&=\frac{14}{2} \\
\\&=7\end{aligned}$
