Question

How do you find the average rate of change for the function `f(x) = x^2 - 2x` on the indicated intervals [1,3]?

Answer 1

The average rate of change of function `f` on interval `[a,b]` is

`(f(b) - f(a))/(b-a)`

Explanation:

So, in this case we have

`f(3) = 9-6 =3` and `f(1) = 1-2=-1`.

And the average rate of change is

`(f(3) - f(1))/(3-1) = (3-(-1))/(3-1) = 4/2 = 2`

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

It is the ratio of the changes, it may also be written `(Deltaf)/(Deltax)` and it may be thought of as the slope of the line through the endpoints of the graph of `f` on the interval.

Algebraically it is one version of the difference quotient. (The quotient of the differences in `f` values and `x` values..)