```Date: Oct 23, 2012 8:53 PM
Author: Doug Kuhlmann
Subject: RE:[ap-calculus] Double Derivatives

NOTE: This ap-calculus EDG will be closing in the next few weeks. Please sign up for the new AP CalculusTeacher Community Forum at https://apcommunity.collegeboard.org/getting-startedand post messages there. ------------------------------------------------------------------------------------------------Debbie,If f ' (a) = 0 and f '' (a)=0 it might be a POI but it does not have to be.  For example, consider f(x)=x^4.f ' (x)=4x^3 and f '' (x)=12x^2 so f ' (0)=0=f '' (0).  But the concavity of f does not change at x=0, so it is not a POI.HTHDoug----------------------------Doug KühlmannMath DeptPhillips AcademyAndover, MA 01810________________________________From: Debbie Bricker [DBricker@cathedralcatholic.org]Sent: Tuesday, October 23, 2012 5:12 PMTo: AP CalculusSubject: [ap-calculus] Double Derivatives?NOTE:This ap-calculus EDG will be closing in the next few weeks. Please sign up for the new AP CalculusTeacher Community Forum at https://apcommunity.collegeboard.org/getting-startedand post messages there.----------------------------------------------------------------------------------------------------------------------------In using the second derivative test for extrema, you may get the second derivative to equal zero when plugging in a critical number and the test then fails.  Will this point then be a POI?DebbieTo search the list archives for previous posts go tohttp://lyris.collegeboard.com/read/?forum=ap-calculus---To search the list archives for previous posts go tohttp://lyris.collegeboard.com/read/?forum=ap-calculus
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