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Topic: Can one "soup-up" the LAW OF THE MEAN in the following way?
Replies: 1   Last Post: Nov 23, 2009 8:33 AM

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Posts: 4
From: ocean grove,N.J.
Registered: 5/14/09
Can one "soup-up" the LAW OF THE MEAN in the following way?
Posted: Jun 16, 2009 3:28 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Let J be a closed interval of real numbers whose length
is finite and positive. Let f be a real valued function
defined on J which has a continuous second derivative at
all points of J.

QUESTION: If P1,P2,P3 are any three distinct and
non-collinear points on the graph f(J), does there always
exist at least one point p on J such that the absolute
value of the curvature of f(J) at the point (p,f(p)) is
greater than or equal to 1/r-where r is the radius of the
circle through the three points P1,P2,P3?

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