## College Algebra (10th Edition)

$-17$
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 $-17$.