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re: inflection points
Posted:
Oct 27, 1994 11:55 AM
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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
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