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

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Posts: 6
Registered: 12/6/04
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

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

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