Question 8 Suppose f: [a , b] → R is a function with no absolute maximum on [a , b] Which of the following must be true?

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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Question 8
Suppose f : [a , b] ·
R is a function with no absolute maximum on [a , b].
Which of the following must be true?
f is not continuous on [a , b] .
f has no absolute minimum on [a , b] .
f is continuous on [a , b] .
O f'(x) does not exist for some x in the open interval (a, b) .
Of does not have any critical points in [a , b] .
Transcribed Image Text:Question 8 Suppose f : [a , b] · R is a function with no absolute maximum on [a , b]. Which of the following must be true? f is not continuous on [a , b] . f has no absolute minimum on [a , b] . f is continuous on [a , b] . O f'(x) does not exist for some x in the open interval (a, b) . Of does not have any critical points in [a , b] .
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