g(x)=-\frac{x^{2}}{4}+7
what is the average rate of change of g over the interval -2,4?

Question

Accepted Answer

# Explanation:
## Step1: Find $g(-2)$
Substitute $x = -2$ into $g(x)=-\frac{x^{2}}{4}+7$.
$$
\begin{align*}
g(-2)&=-\frac{(-2)^{2}}{4}+7\
&=-\frac{4}{4}+7\
&=- 1 + 7\
&=6
\end{align*}
$$
## Step2: Find $g(4)$
Substitute $x = 4$ into $g(x)=-\frac{x^{2}}{4}+7$.
$$
\begin{align*}
g(4)&=-\frac{4^{2}}{4}+7\
&=-\frac{16}{4}+7\
&=-4 + 7\
&=3
\end{align*}
$$
## Step3: Calculate the average rate of change
The formula for the average rate of change of a function $y = g(x)$ over the interval $[a,b]$ is $\frac{g(b)-g(a)}{b - a}$. Here $a=-2$, $b = 4$.
$$
\begin{align*}
\frac{g(4)-g(-2)}{4-(-2)}&=\frac{3 - 6}{4 + 2}\
&=\frac{-3}{6}\
&=-\frac{1}{2}
\end{align*}
$$

# Answer:
$-\frac{1}{2}$

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QUESTION IMAGE

Question

Explanation:

Step1: Find \(g(-2)\)

Step2: Find \(g(4)\)

Step3: Calculate the average rate of change

Answer: