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Re: [apcalculus] Double Derivatives
Posted:
Oct 24, 2012 3:37 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.  What no one has mentioned yet (I don't believe) is that not only does f '' = 0 not guarantee an inflection point, it doesn't guarantee that it's one of those. In other words, one can't look at the graph of a function and conclude that the second derivatives is not zero. Often, students will look at a graph say, it's concave up there so f ''>0. This isn't true. Consider the function f(x) = x^4 + 2x for x > 0 and x^5 + 2x for x <= 0. This function is twice differentiable at 0 and f ''(0) = 0. Yet, if you graph f(x) there is nothing special (at least by its looks) about f(x). That is, there is not an inflection point or a relative extrema there. I think there are some that believe if f '' = 0, then one of those must occur, but that's not true.
Bradley
From: Louis Talman <talmanl@gmail.com<mailto:talmanl@gmail.com>> ReplyTo: Louis Talman <talmanl@gmail.com<mailto:talmanl@gmail.com>> To: AP Calculus <apcalculus@lyris.collegeboard.com<mailto:apcalculus@lyris.collegeboard.com>> Cc: AP Calculus <apcalculus@lyris.collegeboard.com<mailto:apcalculus@lyris.collegeboard.com>> Subject: Re: [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.  A number of people have replied to this question, correctly. But I wish they'd mentioned that their answers reflect an important fact: The meaning of the sentence, "The test fails," is precisely what they're illustrating.
When we say that a test fails, we mean exactly that the test doesn't give us *any* useful information about the phenomenon we used the test for.
On Tue, Oct 23, 2012 at 3:12 PM, Debbie Bricker <DBricker@cathedralcatholic.org<mailto:DBricker@cathedralcatholic.org>> wrote:
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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 Louis A. Talman Department of Mathematical and Computer Sciences Metropolitan State College of Denver
<http://rowdy.mscd.edu/%7Etalmanl>
To search the list archives for previous posts go to http://lyris.collegeboard.com/read/?forum=apcalculus
 To search the list archives for previous posts go to http://lyris.collegeboard.com/read/?forum=apcalculus



