1. The problem statement, all variables and given/known data Find the maximum and minimum values of the function f(x, y) =49 − x^2 − y^2 subject to the constraint x + 3y = 10. 3. The attempt at a solution ∇f = <2x,2y> ∇g = <1,3> ∇f =λ∇g 2x = λ 2y = 3λ 2x = 2y/3 x = y/3 y/3 + 3y = 10 y = 3 x = 1 f(1,3) = 39 Now that is the only point I got, how should I find out whether it is a maximum/minimum/neither? I understand for closed constaints, like x^2 + y^2 =1, but here I don't understand what I am supposed to do. I know that it is a maximum, by looking at the answer key, but I want to understand the process of figuring it out.