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Question: Arnold's problem

Question:Arnold's problem

Markiyan Hirnyk 7759 Maple
January 12 2011
2

      Here is one of the problems from "Mathematical Trivium"  (Russian Mathematical Surveys, 1991, 46:1, 271-278) by V. Arnold. Those problems are aimed at the strong graduate and postgraduate students of the top universities.
      I find it remarkable that a big part of the Arnold's problems can be solved with Maple.
 
      Problem 8."What are the numbers of the maximums, minimums, and saddle points of the function x^4+y^4+z^4+u^4+t^4 on the surface {x+y+z+u+t=0,x^2+y^2+z^2+u^2+t^2=1,x^3+y^3+z^3+u^3+t^3=c}, where c is a real parameter?"

PS. If it would be of interest for the MaplePrimes users, then I will present the next ones.
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