find the average rate of change of g(x) = -3x³ over the interval -3, 1. write your answer as an integer…

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, $a=-3$, $b = 1$, and $g(x)=-3x^{3}$.

Step2: Calculate $g(a)$ and $g(b)$

First, find $g(-3)$: $g(-3)=-3\times(-3)^{3}=-3\times(-27)=81$. Then, find $g(1)$: $g(1)=-3\times(1)^{3}=-3$.

Step3: Substitute into the formula

Substitute $g(-3) = 81$, $g(1)=-3$, $a=-3$, and $b = 1$ into the average - rate - of change formula: $\frac{g(1)-g(-3)}{1-(-3)}=\frac{-3 - 81}{1 + 3}=\frac{-84}{4}=-21$.

Answer:

$-21$