Consider the functions f(x) = x/(x² + 1)ⁿ, 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 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.

Transcribed Image Text:

х3D +- V 2n – 1