5 Steps to a 5 AP Calculus BC 2019

Graphs of Functions and Derivatives 125

(e) A sketch of the graph of fis shown in Figure 7.4-3.

Figure 7.4-3

Example 3

Given the graph of f′in Figure 7.4-4, find where the functionf (a) has a horizontal tan-

gent, (b) has its relative extrema, (c) is increasing or decreasing, (d) has a point of inflection,

and (e) is concave upward or downward.

–2

–2

–5 –4 –3

–3

–1

–1

01 3467895 x

y

1

2

3

4

f ′

2

Figure 7.4-4
(a) f′(x)=0atx=−4, 2, 4, 8. Thus,fhas a horizontal tangent at these values.
(b) Summarize the information of f′on a number line:

The First Derivative Test indicates that fhas relative maximums atx=−4 and 4; and

fhas relative minimums atx=2 and 8.