find the average rate of change of f(x)=-2x^2 - 2x from x = 2 to x = 6. simplify your answer as much as…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 2$, $b = 6$, and $f(x)=-2x^{2}-2x$.

Step2: Calculate $f(6)$

Substitute $x = 6$ into $f(x)$: $f(6)=-2\times6^{2}-2\times6=-2\times36 - 12=-72-12=-84$.

Step3: Calculate $f(2)$

Substitute $x = 2$ into $f(x)$: $f(2)=-2\times2^{2}-2\times2=-2\times4 - 4=-8 - 4=-12$.

Step4: Calculate the average rate of change

$\frac{f(6)-f(2)}{6 - 2}=\frac{-84-(-12)}{4}=\frac{-84 + 12}{4}=\frac{-72}{4}=-18$.

Answer:

$-18$