Which of the following statements are true?(i) Every continuous function f : [a, b] → R has a minimum and maxi-mum point over [a, b](ii) A continuous function f : (a, b] → R can not have a minimum point over (a, b](iii) Every function f : [a, b] → R which has a maximum point over [a, b]has also a minimum point over [a, b](iv) Every differentiable function f : R → R has a minimum point over R(Give precise references to the results in the Lecture Notes for those which are true.Construct counterexamples for those that are false. A clear sketch without a formulasuffices as a counterexample.)
Which of the following statements are true?(i) Every continuous function f : [a, b] → R has a minimum and maxi-mum point over [a, b](ii) A continuous function f : (a, b] → R can not have a minimum point over (a, b](iii) Every function f : [a, b] → R which has a maximum point over [a, b]has also a minimum point over [a, b](iv) Every differentiable function f : R → R has a minimum point over R(Give precise references to the results in the Lecture Notes for those which are true.Construct counterexamples for those that are false. A clear sketch without a formulasuffices as a counterexample.)
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...
Related questions
Question
Which of the following statements are true?
(i) Every continuous function f : [a, b] → R has a minimum and maxi-
mum point over [a, b]
(ii) A continuous function f : (a, b] → R can not have a minimum point
over (a, b]
(iii) Every function f : [a, b] → R which has a maximum point over [a, b]
has also a minimum point over [a, b]
(iv) Every differentiable function f : R → R has a minimum point over R
(Give precise references to the results in the Lecture Notes for those which are true.
Construct counterexamples for those that are false. A clear sketch without a formula
suffices as a counterexample.)
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