Question

Given this equation y = x2 + 2x -5 , Find the average rate of change over the interval 2 ≤ x ≤ 4 ?

Answer 1

The average rate of change is 8.

Explanation:

We are given the equation:

`y=x^2+2x-5`

And we want to find the average rate of change on the interval [2, 4].

When finding the average rate of change, we essentially find the endpoints and then find the slope between them.

So, the endpoints are:

`y(2)=(2)^2+2(2)-5=3`

And:

`y(4)=(4)^2+2(4)-5=19`

So, the average rate of change between them is:

`\displaystyle m=(19-3)/(4-2)=(16)/(2)=8`