Question

What is the average rate of change of the function over the interval x = 0 to x = 8?

f(x)=(2x-2)/(5x-6)
Write your answer as a fraction.

Answer 1

-13/400

Explanation:

The pertinent formula is

change in f(x) over [a, b] f(8) - f(0)

a. r. of change = --------------------------------------- = ----------------

change in x over [a, b] 8 - 0

Continuing these calculations, we get:

2(8) - 2 2(0) - 2 14/8 -2/8

(1/8) -------------- - (1/8) ------------- = ----------- - -----------

5(8) - 6 5(0) - 6 40 - 6 -6

7/4 1/4

This simplifies to average rate of change = ------- - --------

34 6

7 1

= ------------- - ---------- = -13/400

136 24