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For any constant a, let g(x) = ax - 2xin(x) for x > 0.

For any constant a, let g(x) = ax - 2xin(x) for x > 0.

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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For any constant a, let g(x) = ax - 2xln(x) for x > 0. (a) What is the x-intercept g(x)? (²) X = (b) Find g '(x) = e O (c) For what values of a does g(x) have a critical point for x > 0? a> 0 O a ≥ 0 a ≤ 0 -8 < a < 00 X = a < 0 (a- - - 2) - 2 ln(x) (d) Find the x-coordinate of the critical point of g(x). (e) Find g "(x) (f) Use the Second Derivative Test to classify the critical point. g "(critical point) = This means that g(x) is [---Select--- ✓at the critical point because g "(critical point) is ---Select---]. The critical point is [---Select---
Transcribed Image Text:For any constant a, let g(x) = ax - 2xln(x) for x > 0. (a) What is the x-intercept g(x)? (²) X = (b) Find g '(x) = e O (c) For what values of a does g(x) have a critical point for x > 0? a> 0 O a ≥ 0 a ≤ 0 -8 < a < 00 X = a < 0 (a- - - 2) - 2 ln(x) (d) Find the x-coordinate of the critical point of g(x). (e) Find g "(x) (f) Use the Second Derivative Test to classify the critical point. g "(critical point) = This means that g(x) is [---Select--- ✓at the critical point because g "(critical point) is ---Select---]. The critical point is [---Select---
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