Select the correct answer. If f (x) = x^3-x, what is the average rate of change of f (x) over the interval [1, 5]?

Average rate of change = 30

Step-by-step explanation:

We have given a function.

f (x) = x³-x

[a, b] = [1,5]

We have to calculate the average rate of change of f (x) over the given interval.

The formula to calculate the average rate of change of function is:

Average rate of change = f (b) - f (a) / (b-a)

f (b) = f (5) = (5) ³-5

f (b) = f (5) = 125-5

f (b) = f (5) = 120

f (a) = f (1) = (1) ³-1

f (a) = f (1) = 1-1

f (a) = f (1) = 0

Putting values in formula, we have

Average rate of change = 120-0 / 5-1

Average rate of change = 120/4

Average rate of change = 30 which is the answer.