Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

My Maths notes don't explain this, but is there a saddle point or a local maximum?

share|cite|improve this question
up vote 1 down vote accepted

I assume you're trying to classify a stationary point by looking at the matrix of second derivatives? In that case, you can't draw any conclusion if the matrix is semidefinite, because what happens can be influenced by higher-order terms in the Taylor expansion of the function at the critical point. Investigation of what really happens must be done on a case-by-case basis, using whatever methods one might come up with, and since this goes beyond the simple standard methods, it's usually swept under the rug in introductory calculus courses.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.