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(f) Use the Second Derivative Test to classify the critical point. (²) g "(critical point) = X . This means that g(=

(f) Use the Second Derivative Test to classify the critical point. (²) g "(critical point) = X . This means that g(=

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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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)? X = (b) Find g '(x) = (a − 2) - 2 ln(x) (c) For what values of a does g(x) have a critical point for x > 0? O a > 0 O O a ≥ 0 O a ≤0 O -∞ < a < 00 X = a < 0 (d) Find the x-coordinate of the critical point of g(x). (²-1) e (e) Find g "(x) = 2 X (f) Use the Second Derivative Test to classify the critical point. 0-2²) g "(critical point) = e . This means that g(x) is concave down at the critical point because g "(critical point) is negative The critical point is a local maximum
Transcribed Image Text:For any constant a, let g(x) = ax - 2xln(x) for x > 0. (a) What is the x-intercept g(x)? X = (b) Find g '(x) = (a − 2) - 2 ln(x) (c) For what values of a does g(x) have a critical point for x > 0? O a > 0 O O a ≥ 0 O a ≤0 O -∞ < a < 00 X = a < 0 (d) Find the x-coordinate of the critical point of g(x). (²-1) e (e) Find g "(x) = 2 X (f) Use the Second Derivative Test to classify the critical point. 0-2²) g "(critical point) = e . This means that g(x) is concave down at the critical point because g "(critical point) is negative The critical point is a local maximum
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