Question

2.6 score: 11/16 answered: 11/16 question 12 find the average rate of change on the interval. h(x)=4x^3 on -2,1 question help: video ebook written example

Explanation:

Step1: Recall the average - rate - of - change formula

The average rate of change of a function $y = h(x)$ on the interval $[a,b]$ is $\frac{h(b)-h(a)}{b - a}$. Here, $a=-2$, $b = 1$, and $h(x)=4x^{3}$.

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

First, find $h(-2)$:
$h(-2)=4\times(-2)^{3}=4\times(-8)=-32$.
Then, find $h(1)$:
$h(1)=4\times(1)^{3}=4\times1 = 4$.

Step3: Substitute into the formula

Substitute $h(-2)=-32$, $h(1) = 4$, $a=-2$, and $b = 1$ into the average - rate - of change formula $\frac{h(b)-h(a)}{b - a}$:
$\frac{h(1)-h(-2)}{1-(-2)}=\frac{4-(-32)}{1 + 2}=\frac{4 + 32}{3}=\frac{36}{3}=12$.

Answer:

$12$