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

1 Answer
May 22, 2016

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.