Question

Find the absolute maximum and minimum of the function F(x,y)=(x^2)+(y^2)+(4x)-(4y) restricted to the closed unit disk {(x,y): (x^2)+(y^2) < or = to 1}. Also find the absolute maximum and minimum values of F(x,y).

Answer 1

AHH SO HARD XD

Answer 2

I found the point restricted to the interior, but I need help on the Lagrange multipliers.
I get the following sets of equations:
2x+4=lambda(2x)
2y-4=lambda(2y)
(x^2)+(y^2)=1