Question

How do you find the average rate of change of `g(x)=x^2-x+3` over the interval [4, 6]?

Answer 1

9

Explanation:

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

To calculate the average rate of change between the 2 points use.

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

`g(6)=6^2-6+3=33`

and `g(4)=4^2-4+3=15`

Thus the average rate of change between (4 ,15) and (6 ,33) is

`(33-15)/(6-4)=18/2=9`

This means that the average of all the slopes of lines tangent to the graph of g(x) between (4 ,15) and (6 ,33) is 9.