Question 401556: Topic: Maxima and Minima for functions of 2 variables:
Question: Find the critical points of the question below by determining whether it is a saddle point, relative maximum or minimum:
f(x,y) = xy(1-x-y)
Thank-you for your assistance.
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! 
==>  , and
 .
Solving the preceding system above, we get the following c.p.'s
(i) (0,0)
{ii) (1,0)
(iii) (0,1)
(iv) (1/3, 1/3)
Finding the 2nd order partial derivatives:
 , and
(i) At (0,0), 
 , and 
D =  .
Therefore there is a saddle point at (0,0).
(ii) At (1,0),
 , and 
D =  .
Therefore there is a saddle point at (1,0)
(iii) At (0,1), 
, and
D =  .
Therefore there is saddle point at (0,1).
(iv) At (1/3, 1/3), 
 , and 
D =  .
Therefore there is a relative maximum at (1/3, 1/3).
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