Saddle Points and Inflection Points

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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 (March 2011)
Open content licensed under CC BY-NC-SA


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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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