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Saddle Points and Inflection Points


	Theorem: Let be a function with continuous second partial derivatives in a open set in the plane and let be a saddle point in . Then there exists a continuous function with for which the projection on the plane of the intersection of the surface and the cylindrical surface has a inflection point at .


	Contributed by: Soledad Mª Sáez Martínez and Félix Martínez de la Rosa

Take the quadratic form

. For each

and

such that

and

, the function

verifies the theorem.

Reference:
F. Martínez de la Rosa, "Saddle Points and Inflection Points," The College Mathematics Journal, 38(5), 2007 pp. 380–383.

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