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Complete parts a. and b. below. a. Prove that f(x)=x- In x is increasing for x> 1. First, find the derivative. f'(x) = What property of the derivative can be used to show the function is increasing? OA. The derivative approaches to one as x approaches infinity. OB. The derivative is decreasing for x> 1. OC. The derivative is positive for x> 1. OD D. The derivative is undefined at x = 0. b. Using part (a), show that In x1. What can be said about f(x) if it is increasing for x>1? OA. The value of x is increasing, but the value of In x is decreasing. OB. The value of x is growing at the same rate as In x. OC. The difference between x and In x is getting smaller. OD. The difference between x and In x is growing larger. How does this show that Inx1? *** OA. If the value of x is growing at the same rate as In x, then the curves are parallel, where x is greater than In x. OB. If the difference between x and In x is increasing, then x must be greater than In x.

Complete parts a. and b. below. a. Prove that f(x)=x- In x is increasing for x> 1. First, find the derivative. f'(x) = What property of the derivative can be used to show the function is increasing? OA. The derivative approaches to one as x approaches infinity. OB. The derivative is decreasing for x> 1. OC. The derivative is positive for x> 1. OD D. The derivative is undefined at x = 0. b. Using part (a), show that In x1. What can be said about f(x) if it is increasing for x>1? OA. The value of x is increasing, but the value of In x is decreasing. OB. The value of x is growing at the same rate as In x. OC. The difference between x and In x is getting smaller. OD. The difference between x and In x is growing larger. How does this show that Inx1? *** OA. If the value of x is growing at the same rate as In x, then the curves are parallel, where x is greater than In x. OB. If the difference between x and In x is increasing, then x must be greater than In x.

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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Complete parts a. and b. below. a. Prove that f(x)=x- In x is increasing for x> 1. First, find the derivative. f'(x) = What property of the derivative can be used to show the function is increasing? A. The derivative approaches to one as x approaches infinity. B. The derivative is decreasing for x>1. C. The derivative is positive for x> 1. D. The derivative is undefined at x = 0. b. Using part (a), show that In x<xifx>1. What can be said about f(x) if it is increasing for x>1? A. The value of x is increasing, but the value of In x is decreasing. B. The value of x is growing at the same rate as In x. C. The difference between x and In x is getting smaller. D. The difference between x and In x is growing larger. How does this show that In x<xifx>1? A. If the value of x is growing at the same rate as In x, then the curves are parallel, where x is greater than In x. B. If the difference between x and In x is increasing, then x must be greater than In x. meining: 02:36:58
Transcribed Image Text:Complete parts a. and b. below. a. Prove that f(x)=x- In x is increasing for x> 1. First, find the derivative. f'(x) = What property of the derivative can be used to show the function is increasing? A. The derivative approaches to one as x approaches infinity. B. The derivative is decreasing for x>1. C. The derivative is positive for x> 1. D. The derivative is undefined at x = 0. b. Using part (a), show that In x<xifx>1. What can be said about f(x) if it is increasing for x>1? A. The value of x is increasing, but the value of In x is decreasing. B. The value of x is growing at the same rate as In x. C. The difference between x and In x is getting smaller. D. The difference between x and In x is growing larger. How does this show that In x<xifx>1? A. If the value of x is growing at the same rate as In x, then the curves are parallel, where x is greater than In x. B. If the difference between x and In x is increasing, then x must be greater than In x. meining: 02:36:58
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