Module 13 :  Maxima, Minima and Saddle Points, Constrained maxima and minima
Lecture 39 :  Absolute maxima / minima [Section 39.1]
 

As , we have , and hence, the critical points of are given by

Since follows that

Thus, the desired triangle is equilateral.

   
  Practice Exercises
(1)
Find the absolute minimum and the absolute maximum of the function
 

on the closed triangular plate bounded by the lines

  Answer
   
(2)
Find the absolute maximum and the absolute minimum of
 

over the region

  Answer
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