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

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Paul A. Foerster

Posts: 892
Registered: 12/6/04
Re: [ap-calculus] point of inflection question
Posted: Sep 24, 2012 9:05 AM
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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!
> ---
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