Graphs of Functions and Derivatives 109Example 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 7.2-3.)
[–3,8] by [–4,4]
Figure 7.2-3Example 3
The graph of f′on (1, 6) is shown in Figure 7.2-4. Find the intervals on which f is
increasing or decreasing.
Figure 7.2-4(See Figure 7.2-5.)
Figure 7.2-5Thus,fis decreasing on [1, 2] and [5, 6] and increasing on [2, 5].