Let f(x,y)=xy(1-x-y).

Prove that max{f(x,y) | x>0 , y>0} = 1/27 .

I want to use the statement that sais that if f is continous in a compactic set A then f gets its minimum and maximum in A.

I'm not so sure on which compactic set I need to activate this statement...

Hope you'll be able to help me

Thanks in advance