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A family of double-humped functions Consider the functions f(x) = where n is a positive integer. (x? + 1)" a. Show that these functions are odd for all positive integers n. b. Show that the critical points of these functions are x = + 1 for all positive integers n. (Start with the V2n - 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.

A family of double-humped functions Consider the functions f(x) = where n is a positive integer. (x? + 1)" a. Show that these functions are odd for all positive integers n. b. Show that the critical points of these functions are x = + 1 for all positive integers n. (Start with the V2n - 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.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A family of double-humped functions Consider the functions f(x) = where n is a positive integer. (x? + 1)" a. Show that these functions are odd for all positive integers n. b. Show that the critical points of these functions are x = + 1 for all positive integers n. (Start with the V2n - 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:A family of double-humped functions Consider the functions f(x) = where n is a positive integer. (x? + 1)" a. Show that these functions are odd for all positive integers n. b. Show that the critical points of these functions are x = + 1 for all positive integers n. (Start with the V2n - 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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