given the function ( h(x)=-x^{2}-8x + 18 ), determine the average rate of change of the function over the interval ( -8leq xleq2 ).

Question

Accepted Answer

# Explanation:
## Step1: Recall the average rate of change formula
The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-8$, $b = 2$, and $f(x)=-x^{2}-8x + 18$.
## Step2: Calculate $h(-8)$
Substitute $x=-8$ into $h(x)$:
$$
\begin{align*}
h(-8)&=-(-8)^{2}-8\times(-8)+18\
&=-64 + 64+18\
&=18
\end{align*}
$$
## Step3: Calculate $h(2)$
Substitute $x = 2$ into $h(x)$:
$$
\begin{align*}
h(2)&=-(2)^{2}-8\times(2)+18\
&=-4-16 + 18\
&=-2
\end{align*}
$$
## Step4: Compute the average rate of change
Using the formula $\frac{h(2)-h(-8)}{2-(-8)}$, substitute $h(2)=-2$ and $h(-8)=18$:
$$
\begin{align*}
\frac{h(2)-h(-8)}{2-(-8)}&=\frac{-2 - 18}{2 + 8}\
&=\frac{-20}{10}\
&=-2
\end{align*}
$$

# Answer:
$-2$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the average rate of change formula

Step2: Calculate \(h(-8)\)

Step3: Calculate \(h(2)\)

Step4: Compute the average rate of change

Answer: