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

Due to symmetry of the domain, Thus, we need only determine the absolute maximum and minimum of the functions

and

It is easy to check that the function

and

Also,

Finally, we compare these values of

here we have ignored the points and due to symmetry. Thus,

4