question 7\nfind the average rate of change of $g(x)=1x^{3}+4$ from $x = - 2$ to $x = 1$.\nquestion help…
question 7\nfind the average rate of change of $g(x)=1x^{3}+4$ from $x = - 2$ to $x = 1$.\nquestion help: message instructor
Answer
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, $a=-2$, $b = 1$, and $g(x)=x^{3}+4$.
Step2: Calculate $g(a)$ and $g(b)$
First, find $g(-2)$: $g(-2)=(-2)^{3}+4=-8 + 4=-4$. Then, find $g(1)$: $g(1)=1^{3}+4=1 + 4=5$.
Step3: Calculate the average rate of change
Substitute $g(-2)=-4$, $g(1)=5$, $a=-2$, and $b = 1$ into the formula $\frac{g(b)-g(a)}{b - a}$: $\frac{g(1)-g(-2)}{1-(-2)}=\frac{5-(-4)}{1 + 2}=\frac{5 + 4}{3}=\frac{9}{3}=3$.
Answer:
3