MA 3972-MA-Book April 11, 2018 17:21
Graphs of Functions and Derivatives 143[–1, 1] by [–1, 1]
Figure 8.2-2Example 2
Find the critical numbers off(x)=(x−3)^2 /^5.
f′(x)=2
5
(x −3)−^3 /^5 =2
5(x−3)^3 /^5. Note that f′(x) is undefined at x=3 and that
f′(x)=0. Therefore, 3 is the only critical number of f. (See Figure 8.2-3.)
[–3, 8] by [–4, 4]
Figure 8.2-3Example 3
The graph of f′on (1, 6) is shown in Figure 8.2-4. Find the intervals on which f is
increasing or decreasing.
yxf′0 1233456Figure 8.2-4