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RE:[apcalculus] Double Derivatives
Posted:
Oct 23, 2012 8:53 PM


NOTE: This apcalculus EDG will be closing in the next few weeks. Please sign up for the new AP Calculus Teacher Community Forum at https://apcommunity.collegeboard.org/gettingstarted and 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.
HTH
Doug
 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: [apcalculus] Double Derivatives
?
NOTE: This apcalculus EDG will be closing in the next few weeks. Please sign up for the new AP Calculus Teacher Community Forum at https://apcommunity.collegeboard.org/gettingstarted and 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?
Debbie
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