1. 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 : RR 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.) [20 Marks]

1. 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 : RR 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.) [20 Marks]

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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