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Now press (
3
Hit ENTER to obtain the solution:
2.2 Characteristics of Functions
EXAMPLE 5 Using a Graphing Utility to Locate Local Maxima and Minima
and to Determine Where a Function is Increasing and
Decreasing
(a) Use a graphing utility to graph f x
(b) Determine where f is increasing and where it is decreasing.
Solution
(a) Graphing utilities have a feature that finds the maximum or
minimum point of a graph within a given interval. Graph the function f
with Xmin = -2 and Xmax = 2, Xscl = 1, Ymin = -10, Ymax = 30, and
Yscl = 5. You should obtain the following:
)
to obtain:
Determine where f has a local maximum and where f has a local
minimum.
( ) =
−
+
3
6
x
12
x
5
for -2 < x < 2.
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