1. The problem statement, all variables and given/known data Find the maximum and minimum values of f(x,y) = 2x^2+4y^2 - 4xy -4x on the circle defined by x^2+y^2 = 16. 2. Relevant equations Lagrange's method, where f_x = lambda*g_x, f_y= lambda*g_y (where f is the given function and g(x,y) is the circle on which we are looking for the extrema) 3. The attempt at a solution Computed the partials, and was able to end up with an equation like 2y -2 = [itex]\lambda[/itex]*(x-y) From this, critical points look like they might be (1, root 15) and (root 15, 1) but this does not seem to be the answer. Any help at all is much appreciated!