Search All of the Math Forum:

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: re: inflection points
Replies: 1   Last Post: Oct 27, 1994 9:29 PM

 Messages: [ Previous | Next ]
 DAVE_LUNSFORD@gcccd.cc.ca.us Posts: 6 Registered: 12/6/04
re: inflection points
Posted: Oct 27, 1994 11:55 AM

On Thu Oct 27, 1994 Jeff Myers posted:

> Yesterday, during a discussion of concavity, inflection points,
>third derivative tests, etc. in (high school) A. P. Calculus, a
>student asked a question which gets more interesting as I
>investigate it. He wondered if a differentiable function which,
>say, is concave downward for x<0, contains a line segment from
>x=0 to x=1, then is concave upward for x>1 could be said to have
>inflection points or even an "inflection segment."

> .....
>______________________________________________________________________
>Jeff Myers Granville High School Granville, OH
>43023 jmyers@laca.ohio.gov

Having checked 19 calculus texts ranging from Thomas' 2nd edition
to two reform project texts, I find a consistent definition of an
inflection point occurring only at the point where f''(c) = 0 or
fails to exist and where f''(x) changes sign. Since f''(x) = 0
on [0, 1], no sign change takes place, hence, no inflection
point.

dave_lunsford@gcccd.cc.ca.us

Date Subject Author
10/27/94 DAVE_LUNSFORD@gcccd.cc.ca.us
10/27/94 gjporter@math.upenn.edu