Consider the function ƒ(x, y) = x2 + y2 + 2xy - x - y + 1 over the square 0 <=x <= 1 and 0<= y <=1.
a. Show that ƒ has an absolute minimum along the line segment 2x + 2y = 1 in this square. What is the absolute minimum value?
b. Find the absolute maximum value of ƒ over the square.