Average Function Value

If a function is continuous on a closed interval [a, b], there exists a point, c, inside the interval such that:

Average Function Value

Average Function Value

Examples

1. Find the value of c, the average function value, of the function f(x) = 3x2 on the interval [−4, −1].

Since the function is continuous on the interval [−4, −1], the average function value can be applied.

Average Function Value Example

Average Function Value Operations

Average Function Value Solution

The positive solution is not valid because it does not belong to the interval.


2. Is the average function value applicable to the following function in the interval [0, 1]?

Average Function Value Example

Since the function is continuous on the interval [0, 1], the average function value is applicable and can be applied.

Average Function Value Example

Average Function Value Operations

Average Function Value Solution