Question

How do you find the average rate of change of `g(x) = 3 + 1/2x` from [1,8]?

Answer 1

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

Explanation:

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.)

For this problem you find

`(g(8)-g(1))/(8-1)`