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Math 1314
Lesson 13
Absolute Extrema
In earlier sections, you learned how to find relative (local) extrema.
These points were
the high points and low points relative to the other points around them.
In this section,
you will learn how to find
absolute extrema
, that is the highest high and/or the lowest
low on the domain of the function, or on a specific closed interval.
Absolute Extrema on the Domain of
f
Definition:
If
)
(
)
(
c
f
x
f
≤
for all
x
in the domain of
f
, then
f
(c) is called the
absolute
maximum value
of
f
.
If
)
(
)
(
c
f
x
f
≥
for all
x
in the domain of
f
, then
f
(c) is called the
absolute minimum value
of
f
.
Sometimes you will be asked to find the absolute extrema over the interval
( 29
∞
∞

,
.
Example 1
:
State the absolute maximum and/or absolute minimum value(s).
Example 2
:
State the absolute maximum and/or absolute minimum value(s).
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View Full Document As you can see from these two examples, the absolute extrema
may or may not exist.
To
find absolute extrema on
( 29
∞
∞

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This note was uploaded on 02/21/2012 for the course MATH 1314 taught by Professor Marks during the Fall '08 term at University of Houston.
 Fall '08
 MARKS
 Math

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