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RE: [apcalculus] point of inflection question
Posted:
Sep 23, 2012 12:50 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.  I would argue that y=x^(1/3) has a point of inflection at the origin, even thought the function is not differentiable there. While a function that changes concavity via a "corner" does not have a point of inflection at said point. "My" defn of an inflection point is a "smooth change in concavity". This allows for vertical tangents, but not cusps and certainly not points of discontinuity. Of course, then my students ask what I mean by "smooth", which is a good thing!
Bradley
"...each day's a gift and not a given right Leave no stone unturned, leave your fears behind And try to take the path less traveled by That first step you take is the longest stride."
Nickelback ________________________________________ From: Brett Baltz [brettbaltz@msdlt.k12.in.us] Sent: Sunday, September 23, 2012 7:41 AM To: AP Calculus Subject: [apcalculus] point of inflection question
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.  I find conflicting reports on this, which leads me to believe there may be conflicting opinions or varying explanations among textbooks. For that reason, I assume this question would not be addressed in this way on the exam.
Can a point of inflection be identified where the function has a vertical asymptote just because the concavity changes? For example does y=1/x have a point of inflection at x=0? My belief is that a point of inflection cannot exist at a point where the function is not defined or even not differentiable.
The debate in my head has carried over into the classroom.
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 To search the list archives for previous posts go to http://lyris.collegeboard.com/read/?forum=apcalculus



