Question

Find the average rate of change​

Answer 1

`\huge\boxed{16}`

To find the average rate of change on a domain, you find the points on the line at the ends of the domain, then find the slope between the points.

We'll start by finding the points on the function graph at the ends of the domain.

These are
`(-3,g(-3))` and
`(1,g(1))`.

Substitute and solve:

`\displaystyle g(-3)=2(-3)^3+(9)/((-3)^2)=2(-27)+(9)/(9)=-54+1=\boxed{-53}`

`\displaystyle g(1)=2(1)^3+(9)/(1^2)=2(1)+(9)/(1)=2+9=\boxed{11}`

This means the points at the ends of the domain are
`(-3,-53)` and
`(1,11)`.

To find the average rate of change, all we need to do is find the slope between these points.

The slope is defined as rise over run, or:

`(y_2-y_1)/(x_2-x_1)`

Substitute
`(x_1,y_1)` and
`(x_2,y_2)` with the points we found:

`(11-(-53))/(1-(-3))=(11+53)/(1+3)=(64)/(4)=\boxed{16}`