Question

How do you find the average rate of change of `f(x)=x^2-6x+8` over the interval [4,9]?

Answer 1

7

Explanation:

The`color(blue)" average rate of change"` of f(x) over an interval between 2 points (a ,f(a)) and (b ,f(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)((f(b)-f(a))/(b-a))color(white)(a/a)|)))`

`f(9)=9^2-6(9)+8=35`

and `f(4)=4^2-6(4)+8=0`

The average rate of change between (4 ,0) and (9 ,35) is

`(35-0)/(9-4)=35/5=7`

This means that the average of all the slopes of lines tangent to the graph of f(x) between (4 ,0) and (9 ,35) is 7.