Question

Find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value.

f (x) = x^3,       [0, 1]

Answer 1

Step 1:

The function

Average value of the function on is defined as .

In this case .

Average value of

Step 2:

Equate the function to its average value.

Solution:

Average value is .

.