Question

How do you find the average rate of change of `f(x)= -1/x` from [1,2]?

Answer 1

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

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..)

In this case

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