Question

How do you find the average rate of change of `y=-1/(x-2)` over [-3,-2]?

Answer 1

The average rate of change of `y=−1/(x−2)` over `[-3,-2]` equals `1/20`

Explanation:

The rate of change of `y(x)` over the interval `[x_1,x_2]` is defined as the ratio between the variation of `y(x)` and the variation of `x` over the interval, so that:

`R= (Deltay)/(Deltax) = (y(x_2)-y(x_1))/(x_2-x_1)`

In our case:

`R = ((-1/(-2-2))-(-1/(-3-2)))/((-2)-(-3))= (1/4-1/5)=1/20`