Question

homework assignment 3.3 rates of change and behavior of graphs
score: 1/11 answered: 1/11
question 3
find the average rate of change of $g(x)=1x^{3}-4$ from $x = - 1$ to $x = 4$.
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Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = g(x)$ from $x = a$ to $x = b$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a=-1$, $b = 4$, and $g(x)=x^{3}-4$.

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

First, find $g(-1)$:
$g(-1)=(-1)^{3}-4=-1 - 4=-5$.
Then, find $g(4)$:
$g(4)=4^{3}-4=64 - 4=60$.

Step3: Calculate the average rate of change

Substitute $g(-1)=-5$, $g(4)=60$, $a=-1$, and $b = 4$ into the formula $\frac{g(b)-g(a)}{b - a}$:
$\frac{g(4)-g(-1)}{4-(-1)}=\frac{60-(-5)}{4 + 1}=\frac{60 + 5}{5}=\frac{65}{5}=13$.

Answer:

$13$