Given function f(x, y) = x 2 + xy + y 2 + y (1) locate critical points (2) classify those critical point (determine it’s local max or local min)

Set both partial derivatives equal to zero and solve for .



The Hessian matrix (matrix of second-order partial derivatives) for this function is



Now since for any , and for any , it follows by the second partial derivative test that the critical point is the site of a local minimum of . The value of the minimum is .