College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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![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.
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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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