# How do you find the absolute extrema of the function on the indicated interval by using the concept of the Extreme-Value Theorem f(x) = { |x| if -3 ≤ x ≤ 2 , 4-x if 2 < x ≤ 3 ; [ -3, 3]?

##### 1 Answer

#### Answer:

The minimum is

The maximum is

#### Explanation:

Note first that this function is continuous on

The only possible "problem point" is

Thus, the Extreme Value Theorem guarantees that the function attains both a minimum and a maximum on the interval.

These extrema occur at values of

(Values of

For the function in this question, we get the following piecewise defined derivative:

**Note:**

The only critical numbers are

The minimum and the maximum must occur at one of the values of

Evaluating

The minimum is

The maximum is

Some teachers and textbooks express this by writing:

Minimum:

Maximum: