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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

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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Saddle Points and Inflection Points