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3.3 Let g(x) be a function defined for all x in R, and X₁ and X₂ be real num with x₁ < x₂. Use the information in the given diagram below to answer th following questions. g'(x) <0 glaxxo g'(x) >0 g"(x) >o g"(x) <0 g"(x) >0 1X1 x x

3.3 Let g(x) be a function defined for all x in R, and X₁ and X₂ be real num with x₁ < x₂. Use the information in the given diagram below to answer th following questions. g'(x) <0 glaxxo g'(x) >0 g"(x) >o g"(x) <0 g"(x) >0 1X1 x x

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3.3 Let g(x) be a function defined for all x in R, and x, and x, be real numbers with x, < x₂. Use the information in the given diagram below to answer the following questions. g(x) <0 g'uzxo I д'їх g'(x) >0 20 g"(x) > 0 g" (x) <0 (x) >0 1X1 g їхі x
Transcribed Image Text:3.3 Let g(x) be a function defined for all x in R, and x, and x, be real numbers with x, < x₂. Use the information in the given diagram below to answer the following questions. g(x) <0 g'uzxo I д'їх g'(x) >0 20 g"(x) > 0 g" (x) <0 (x) >0 1X1 g їхі x
a) Determine, with justification, whether the statement is true or false. "(x₁, g(x)) is a critical point of g(x) if and only if g'(x₁) = 0.” b) Is the point (x₂, g(x₂)) a local maximum of g(x)? Justify your answer. Draw a possible graph of g(x). c)
Transcribed Image Text:a) Determine, with justification, whether the statement is true or false. "(x₁, g(x)) is a critical point of g(x) if and only if g'(x₁) = 0.” b) Is the point (x₂, g(x₂)) a local maximum of g(x)? Justify your answer. Draw a possible graph of g(x). c)
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