tangent plane

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1 total messages Started by Julio Kuplinsky Fri, 18 Dec 1992 16:34

#172

Author: Julio Kuplinsky
Date: Fri, 18 Dec 1992 16:34

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Can anyone point me to a source that discusses this problem (which
should be well known, I guess)?

Let f:R^2 ---> R be a function of type C1 with a local minimum at
(0,0) and f(0,0)=0. Suppose that you start pouring water right above
0, and at some point the water starts to spill, say when the depth of
the water is h. Is it true that there is a point (x,y) with f(x,y) =h 
where the tangent plane to f is horizontal? 

J. Kuplinsky

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