Answer
$19$
Work Step by Step
Given: $f(x)=3 x^{2}-2 x+4$
Evaluate $f(3)$ and $f(4)$ to obtain:
\begin{align*}
f(4)&=3(4^2)-2(4)+4\\
&=3(16)-8+4\\
&=48-8+4\\
&=44\\
\\
\\f(3)&=3(3^2)-2(3)+4\\
&=3(9)-6+4\\
&=27-6+4\\
&=25
\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 these values into the formula gives the average of change:
$=\dfrac{44-25}{4-3} \\$
$=\dfrac{19}{1} \\$
$ =19$
