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
Snapshots
Details
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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