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Topic: [ap-calculus] Double Derivatives
Replies: 3   Last Post: Oct 23, 2012 10:30 PM

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Gregory Field

Posts: 12
Registered: 7/8/10
Re: [ap-calculus] Double Derivatives
Posted: Oct 23, 2012 8:52 PM
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Debbie,
     Not always.   In order to determine whether or not the x-coordinate is the x-coordinate of a POI you need to check the sign of the second derivative on either side of that x-coordinate.  My students often ask me that question.  That is when we examine the function f(x) = x^4.  f " (x) = 0 @ x = 0, but the concavity does not change at x = 0, and therefore not a POI.  We then go back to the first derative test and see that the first derivative changes signs from negative to positive at x = 0, thus giving us a relative min of 0 at x = 0.
 
I hope that helps ,
 
Greg Field
Grayson High School
Loganville, GA
 



________________________________
From: Debbie Bricker <DBricker@cathedralcatholic.org>
To: AP Calculus <ap-calculus@lyris.collegeboard.com>
Sent: Tuesday, October 23, 2012 5:12 PM
Subject: [ap-calculus] Double Derivatives


Double Derivatives
 
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Teacher Community Forum at https://apcommunity.collegeboard.org/getting-started
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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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