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

Explanation:

Step1: Recall average rate - of - change formula

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, $a=-2$, $b = 4$, and $g(x)=-\frac{x^{2}}{4}+7$.

Step2: Calculate $g(-2)$

Substitute $x=-2$ into $g(x)$: $g(-2)=-\frac{(-2)^{2}}{4}+7=-\frac{4}{4}+7=-1 + 7=6$.

Step3: Calculate $g(4)$

Substitute $x = 4$ into $g(x)$: $g(4)=-\frac{4^{2}}{4}+7=-\frac{16}{4}+7=-4 + 7=3$.

Step4: Calculate the average rate of change

Use the formula $\frac{g(b)-g(a)}{b - a}=\frac{g(4)-g(-2)}{4-(-2)}$. Substitute $g(-2)=6$ and $g(4)=3$: $\frac{3 - 6}{4+2}=\frac{-3}{6}=-\frac{1}{2}$.

Answer:

$-\frac{1}{2}$