Consider the functions f(x) = x/(x 2 + 1) n , where n is a positive integer.
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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
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Related Book For
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
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