College Algebra & Trigonometry, 2018a

4.3. MAXIMUM AND MINIMUM VALUES 197
4.3 Maximum and Minimum Values
Finding the maximum and minimum values of a function can be very useful
in applications. This is usually referred to as “optimization.” Later on, we will
examine the use of optimization in application problems. For now, we will use
graphs to find the maximum and minimum values of the function.
In the example below, the maximum function value in the region shown is 100.
This occurs where x =2.5.
100
75
50
25
1 2 3 4 5 6
In the graph below, the function shows a maximum value of 5 at x = −1 and a
minimum value of −27 at x =3.
5
−3 −2 −1
−5
1 2 3 4 5
−10
−15
−20
−25