Quiz (Extreme Values of a Continuous Function)

Show all work and justify each step.

(1) Find the critical numbers of the given functions.



(2) Find the absolute maximum and absolute minimum values of the given function on the given interval.



    
(3) Show that is a critical number of the function but does not have a relative extremum at

(4) Consider the cubic function where Show that can have zero, one, or two critical numbers and give examples of each.

(5) Explain why the function must attain a minimum in the open interval

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