What is the average rate of change for the function over the interval, f(x) = 3/(x - 2) between x = 4 and x = 7?

Solution:

Given f(x)= 3 / x - 2 and the interval (4, 7)

The average rate of change of a function

f(x) over the interval [a, b]is = f(b) - f(a) / b - a

Here, f(x) = 3/x - 2

f(b) = f(7) = 3/7 - 2 = 3/5

f(a) = f(4) = 3 / 4 - 2 = 3/2

Therefore, the rate of change is {3/5 - 3/2} / 7 - 4

Rate of change = (-9/10) / 3

Rate of change = -3/10

What is the average rate of change for the function over the interval, f(x) = 3/(x - 2) between x = 4 and x = 7?

Summary: 

The average rate of change for the function over the interval, f(x) = 3/(x - 2) between x = 4 and x = 7 is -3/10.