A family of double-humped functions Consider the functions
Chapter 4, Problem 82(choose chapter or problem)
A family of double-humped functions Consider the functions f 1x2 = x>1x2 + 12n, where n is a positive integer. a. Show that these functions are odd for all positive integers n. b. Show that the critical points of these functions are x = { 1 22n - 1 , for all positive integers n. (Start with the special cases n = 1 and n = 2.) c. Show that as n increases, the absolute maximum values of these functions decrease. d. Use a graphing utility to verify your conclusions.
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