Question

Consider the function
f (x, y) = 25x2+ 25y2- 25xy + 25x - 25y that defined over the region {(x, y)|(x, y) ÎR 2,x > 0, y > 0}.
(i) Determine all the critical points of the function

(ii) Classify the critical points of the function

as a local minimum, local
maximum or a saddle point.