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Re: [apcalculus] point of inflection question
Posted:
Sep 24, 2012 9:05 AM


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.  Bret, et al. 
Lin and Bradley have given good but slightly different answers to what constitutes a point of inflection.
First of all, there must be a "point" for there to be a point of inflection. I presume that the AP readers will take this into account in reading students' responses.
Next, if you use the English (as in "England," not US English), the word is "inflexion," which connotes "not flexed." Using this logic, there would have to be a (unique) tangent at a point of inflection, although the tangent could be vertical. Hence, Bradley's definition makes sense.
However, I prefer a simpler definition, a point of inflection is a point (on the graph, not just an xvalue) at which the concavity changes sign. This is essentially what Lin is saying.
For the next edition of my calculus text (Key Curriculum Press, now Kendall Hunt), I am considering distinguishing between a point of inflection and a "corner point." Right now I am ambivalent.
Regards, Paul TEacher Emeritus of Mathematics Alamo Heights High School San Antonio

> 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



