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College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Functions And Their Graphs
Section2.4: A Library Of Parent Functions
Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...
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业
y
20
ЕXAMPLE 8
Find the absolute maximum and minimum values of the function below.
rX) = x - 3x2 +3
15
2.
SOLUTION
Since f is continuous on
we can use the Closed Interval Method:
10
2]
F(x) =
x3 - 3x2 + 3
F(x) 3x-6x
%3D
-1
1.
4
9.
Since f(x) exists for all x, the only critical numbers of f occur when f'(x) =14
that
is, x = 0 or x = |2
. Notice that each of these critical numbers lies in
The
2
values of fat these critical numbers are
(0) = 3
)
and
(2) = |-1
The values of f at the endpoints of the interval are
and
(4) = 19
2.
Comparing these four numbers, we see that the absolute maximum value is (4) = 19
and the absolute minimum value is f(2) = |-1
Note that in this example the absolute maximum occurs at an endpoint, whereas the absolute
minimum occurs at a critical number. The graph of fis sketched in the figure.
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人
étv A
30
MacBook Air
3.
Transcribed Image Text:https://www.webassign.net/web/Student/Assignment-Respons E 业 y 20 ЕXAMPLE 8 Find the absolute maximum and minimum values of the function below. rX) = x - 3x2 +3 15 2. SOLUTION Since f is continuous on we can use the Closed Interval Method: 10 2] F(x) = x3 - 3x2 + 3 F(x) 3x-6x %3D -1 1. 4 9. Since f(x) exists for all x, the only critical numbers of f occur when f'(x) =14 that is, x = 0 or x = |2 . Notice that each of these critical numbers lies in The 2 values of fat these critical numbers are (0) = 3 ) and (2) = |-1 The values of f at the endpoints of the interval are and (4) = 19 2. Comparing these four numbers, we see that the absolute maximum value is (4) = 19 and the absolute minimum value is f(2) = |-1 Note that in this example the absolute maximum occurs at an endpoint, whereas the absolute minimum occurs at a critical number. The graph of fis sketched in the figure. Need Help? Read It Submit Answer 人 étv A 30 MacBook Air 3.
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