Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



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.
Thanks!  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



