Answer
$-17$
Work Step by Step
RECALL:
A function's average rate of change from $x=a$ to $x=b$ is given by the formula:
$\text{average rate of change} = \dfrac{f(b)-f(a)}{b-a}$
Use the formula above to obtain:
$\text{average rate of change}
\\= \dfrac{f(3)-f(2)}{3-2}
\\=\dfrac{(3\cdot 3 - 4\cdot 3^2)-(3\cdot 2 - 4\cdot 2^2)}{1}
\\=\dfrac{(9-4\cdot9)-(6-4\cdot4)}{1}
\\=\dfrac{(9-36)-(6-16)}{1}
\\=\dfrac{-27-(-10)}{1}
\\=\dfrac{-27+10}{1}
\\=\dfrac{-17}{1}
\\=-17$
Thus, the average rate of change of the given function from $x=2$ to $x=3$ is $-17$.
