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

If $\bigtriangledown^2f = 0 $ in some region in the space, then $f$ cannot have maximum or minimum on that region.

My approach was to assume $f$ has a maximum and then use the second derivative test to obtain a contradiction. Is this a right approach? Is there an easy way to tackle this problem?

share|cite|improve this question
    
It's hard to know if your approach is right, since you didn't give any of the details. – Nate Eldredge Nov 1 '12 at 3:43
2  
haha i don't wanna be 'that guy' but do you want $f$ nonconstant, and the region connected :p? – uncookedfalcon Nov 1 '12 at 4:46

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.