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Topic: [ap-calculus] point of inflection question
Replies: 1   Last Post: Sep 23, 2012 12:50 PM

 Bradley Stoll Posts: 1,300 Registered: 12/6/04
RE: [ap-calculus] point of inflection question
Posted: Sep 23, 2012 12:50 PM

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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!

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From: Brett Baltz [brettbaltz@msdlt.k12.in.us]
Sent: Sunday, September 23, 2012 7:41 AM
To: AP Calculus
Subject: [ap-calculus] point of inflection question

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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
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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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