Answer
$3$
Work Step by Step
The formula for the average rate of change of $f(x)$ from $a$ to $b$ is $\dfrac{f(b)-f(a)}{b-a}.$
Hence, the average rate of change of$f(x)$ from $-2$ to $2$ is:
$=\dfrac{f(2)-f(-2)}{2-(-2)}\\
=\dfrac{[2^4-7\cdot 2^2+3\cdot2+9]-[(-2)^4-7\cdot(-2)^2+3\cdot(-2)+9]}{4}\\
=\dfrac{(16-28+6+9)-(16-28+(-6)+9)}{4}\\
=\dfrac{3-(-9)}{4}\\
=\dfrac{12}{4}\\
=3$
