1. Find the average rate of change of the function, f(x) = log2 (4x) on the interval of x = 2 to x = 8

Given:

It is given that the function is

We need to determine the average rate of change of the function over the interval x = 2 to x = 8.

Value of f(2):

Substituting x = 2 in the function, we get;

Thus, the value of f(2) is 3.

Value of f(8):

Substituting x = 8 in the function, we get;

Thus, the value of f(8) is 5.

Average rate of change:

The average rate of change can be determined using the formula,

Substituting a = 2 and b = 8 in the above formula, we get;

Thus, the average rate of change over the interval x = 2 to x = 8 is