Find the average rate of change of f(x) = 2x^2 + 2 over each of the following intervals.

Question

(a) From 1 to 3.

(b) From 2 to 4.

(c) From -2 to 1.

(a) The average rate of change from 1 to 3 is 8.

(b) The average rate of change from 2 to 4 is.

Answer 1

Every one of these can be done using the same method.

1. First, remember the equation for the average rate of change which determines how much a function changes over a given interval from a to b.
2. f(b) - f(a) / b - a
3. Second, find the values corresponding to f(b) and f(a). You are given b and a already. For the first one a = 1 and b = 3
4. So for f(a) , a = 1
5. This means f(1) = 2 (1)^2 + 2
6. For f(b), b = 3
7. This means f(3) = 2 (3)^2 + 2
8. Lastly, you just plug in the values you find into the average rate of change equation and you will have your answers.

Answer 2

(a) [f(3) - f(1)] / (3 - 1)

Do the others the same way.