Question

How do you find the average rate of change of `h(x)=x^2+3x-1` over [0,2]?

Answer 1

`5`

Explanation:

The average rate of change of the function h(x) over the interval between 2 points (a , h(a)) and (b ,h(b)) is the `color(blue)"slope of the secant line"` connecting the points.

It is found using.

`color(red)(bar(ul(|color(white)(2/2)color(black)((h(b)-h(a))/(b-a))color(white)(2/2)|)))`

`h(b)=h(2)=2^2+3(2)-1=9`

`h(a)=h(0)=-1`

`rArr(9-(-1))/(2-0)=10/2=5`

This means that the average of all the slopes of tangents between (2 ,9) and (0 ,-1) is 5