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 .

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

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.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.