Question

How do you find the average rate of change for the function `f(x)=x^(+2)` on the indicated intervals [4,6]?

Answer 1

The average rate of change of a function `f` on an interval `[a,b]` is `(f(b) - f(a))/(b-a)`

Explanation:

For `f(x)=x^2` on the interval [4,6],

The average rate of change is:

`(f(6) - f(4))/(6-4) = ((6)^2-(4)^2)/2 = 20/2 = 10`

Note that the average rate of change is also the slope of the line through the point on the graph of `f` where `x=4` and where `x=6`. That is, through the points: `(4,16)` and `(6, 36)`