Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Math Forum
»
Discussions
»
Math Topics
»
geometry.research
Notice: We are no longer accepting new posts, but the forums will continue to be readable.
Topic:
Can one "soupup" the LAW OF THE MEAN in the following way?
Replies:
1
Last Post:
Nov 23, 2009 8:33 AM



static
Posts:
4
From:
ocean grove,N.J.
Registered:
5/14/09


Can one "soupup" the LAW OF THE MEAN in the following way?
Posted:
Jun 16, 2009 3:28 PM


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 noncollinear 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/rwhere r is the radius of the circle through the three points P1,P2,P3? STATIC.



