Consider f(x, y) = xy - 2x + 2y + 1 on the triangular region R with vertices (0,0), (0,6), and (-6,0). (0,6) L 3 L2 R (-6,0) (0,0) If (a,b) is the critical point of f, evaluate f(a, b). fla, b) = If La is the line segment connecting points (-6,0) and (0,6), find the maximum and minimum val f f on L3. maximum value of f on L3 = minimum value of f on L3 = Find the extreme values of f on the region R. (Do not forget to consider the extrema of f on L d L2)