5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book May 8, 2018 13:46

Review of Precalculus 71

Example 1

f(x)=x^3 − 3 x+ 2

The functionf(x)=x^3 − 3 x+2 is increasing on (−∞,−1) and (1,∞) and decreasing on
(−1, 1). A relative minimum value of the function is 0, occurring at the point (1, 0), and a
relative maximum value of 4 is located at the point (−1, 4). (See Figure 5.4-2.)

[−8, 8] by [−5, 5]

Figure 5.4-2

Example 2

g(x)=(x−1)^3

Note thatg(x)=(x−1)^3 is increasing for the entire domain (−∞,∞), and it has no relative
minimum or relative maximum values. (See Figure 5.4-3.)

[−5, 5] by [−4, 4]

Figure 5.4-3

Example 3

f(x)=

x

x− 2

The function f is decreasing on the intervals (−∞, 2) and (2,∞), and it has no relative
minimum or relative maximum values. (See Figure 5.4-4.)

[−5, 5] by [−4, 4]

Figure 5.4-4