First Derivative Test is not exhaustive Sketch the graph of a(simple) nonconstant function f that has a local maximum atx = 1, with f′(1) = 0, where f′ does not change sign frompositive to negative as x increases through 1. Why can’t the FirstDerivative Test be used to classify the critical point at x = 1 as alocal maximum? How could the test be rephrased to account forsuch a critical point?

First Derivative Test is not exhaustive Sketch the graph of a(simple) nonconstant function f that has a local maximum atx = 1, with f′(1) = 0, where f′ does not change sign frompositive to negative as x increases through 1. Why can’t the FirstDerivative Test be used to classify the critical point at x = 1 as alocal maximum? How could the test be rephrased to account forsuch a critical point?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 78E

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