# 12.8.2. Maximum and Minimum Values

Determine the absolute maximum and minimum values of the function on the interval .

• A The absolute maximum equals , and the absolute minimum equals .
• B The absolute maximum equals , and the absolute minimum equals .
• C The absolute maximum equals , and the absolute minimum equals .
• D The absolute maximum equals , and the absolute minimum equals .

### Example

Determine the absolute maximum and minimum values of the function on the interval .

### Solution

First, find as follows:

Since is defined for all in the interval , if the function has critical points, they occur when . Now substitute 0 for in the equation and attempt to solve for .

The statement is false, so can never be equal to 0, and the function does not have any critical points. For this reason, it is only necessary to check the endpoints of the interval , which are and . Check by substituting 2 for in the equation .

Next, check by substituting 6 for in the equation .

Thus, the function's absolute maximum is , and its absolute minimum is .

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