Question

homework assignment 3.3 rates of change and behavior of graphs score: 2/11 answered: 2/11 question 4 find the average rate of change of $g(x)=6x^{2}-\frac{8}{x^{3}}$ on the interval $-2,1$. question help: video written example message instructor submit question

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = g(x)$ on the interval $[a,b]$ is $\frac{g(b)-g(a)}{b - a}$, where $a=-2$ and $b = 1$.

Step2: Calculate $g(1)$

Substitute $x = 1$ into $g(x)=6x^{2}-\frac{8}{x^{3}}$.
$g(1)=6\times1^{2}-\frac{8}{1^{3}}=6 - 8=-2$.

Step3: Calculate $g(-2)$

Substitute $x=-2$ into $g(x)=6x^{2}-\frac{8}{x^{3}}$.
$g(-2)=6\times(-2)^{2}-\frac{8}{(-2)^{3}}=6\times4-\frac{8}{-8}=24 + 1=25$.

Step4: Calculate the average rate of change

Using the formula $\frac{g(b)-g(a)}{b - a}$, we have $\frac{g(1)-g(-2)}{1-(-2)}=\frac{-2 - 25}{1 + 2}=\frac{-27}{3}=-9$.

Answer:

$-9$