Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.

Math Forum » Discussions » Courses » ap-calculus

Topic: [ap-calculus] point of inflection question
Replies: 1   Last Post: Sep 24, 2012 9:05 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View  
Paul A. Foerster

Posts: 892
Registered: 12/6/04
Re: [ap-calculus] point of inflection question
Posted: Sep 24, 2012 9:05 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

This ap-calculus 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/getting-started
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 x-value) 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.

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=ap-calculus

To search the list archives for previous posts go to

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum 1994-2015. All Rights Reserved.