Concerning the function f (x, y) = 4x + 6y − 12 − x2 − y2: (a) There is a unique critic...

Concerning the function f (x, y) = 4x + 6y − 12 − x² − y²:

(a) There is a unique critical point. Find it.

(b) By considering the increment , determine whether this critical point is a maximum, a minimum, or a saddle point.

(c) Now use the Hessian criterion to determine the nature of the critical point.