Question

Find the average rate of change on the interval (SHOW ALL WORK)

Answer 1

First, evaluate the function at the ends of the interval:

`\begin{gathered} g(x)=x^3-2x \\ g(-1)=(-1)^3-2(-1) \\ g(-1)=-1^{}+2 \\ g(-1)=1 \end{gathered}`
`\begin{gathered} g(x)=x^3-2x \\ g(2)=2^3-2(2) \\ g(2)=8-4 \\ g(2)=4 \end{gathered}`

Now, the average rate of change will be

`\begin{gathered} \text{Average rate of change }=(g(2)-g(-1))/(2-(-1)) \\ \text{Average rate of change }=(4-1)/(2-(-1)) \\ \text{Average rate of change }=(3)/(2+1) \\ \text{Average rate of change }=(3)/(3) \\ \text{Average rate of change }=1 \end{gathered}`