Answer
$-17$
Work Step by Step
Given:
$$f(x)=3 x-4 x^{2} \\
$$
Evaluate $f(3)$ and $f(2)$ to obtain:
\begin{align*}
f(3)&=3(3)-4(3^2)\\
&=9-4(9)\\
&=9-36\\
&=-27\\
\\
\\f(2)&=3(2)-4(2^2)\\
&=6-4(4)\\
&=6-16\\
&=-10
\end{align*}
The average rate of change from $a$ to $b$ is given by the formula
\[
\begin{array}{l}
\dfrac{f(b)-f(a)}{b-a} \\
\end{array}
\]
Substituting $f(b)=f(3)=-27, f(a)=f(2)=-10, a=2, \text{ and } b=3$ into the formula above gives:
\begin{align*}&=\dfrac{f(3)-f(2)}{3-2}\\
\\&=\dfrac{-27-(-10)}{1}\\
\\&=-27-(-10)\\
\\&=-27+10\\
\\&=-17
\end{align*}
