Let f : [−1, 1] → R be defined by f (x) = x 3 − x.
(a) Find the global maximum and minimum values of f. Justify your answer, rigorously.
(b) Consider instead that f was defined on the domain R instead of [−1, 1] (that is, f : R → R). Would the global maximum and minimum values be the same as in part (a)? Why, or why not?
(c) What is the largest interval domain [a, b] (that is, suppose that the domain of f is [a, b] instead of [−1, 1]) for which the global maximum and minimum values of f remains the same as the answer in part (a)?