EXAMPLE B Find the absolute maximum and minimum values of the function below ra ti 4 14 SOLUTION Since fis continuous on F x x 3x 1 F 0 Since Fix exists for all x the only critical numbers of foccur when The values of fat these critical numbers are we can use the Clesed Interval Method that is Notice that each of these critical numbers lies in K 0 and 2 The values off at the endpoints of the interval are 0 and 4 Comparing these four numbers we see that the absolute masimum value is 4 and the absolute minimum value is 2 Note that in this example the absolute maximum occurs at an endpoint whereas the absolute minimum occurs at a critical number The graph of fis sketched in the