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

HTH

Doug

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Doug Kühlmann

Math Dept

Phillips Academy

Andover, MA 01810

________________________________

From: Debbie Bricker [DBricker@cathedralcatholic.org]

Sent: Tuesday, October 23, 2012 5:12 PM

To: AP Calculus

Subject: [ap-calculus] Double Derivatives

?

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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?

Debbie

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