1. The problem statement, all variables and given/known data Use lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist. f(x,y) = x+3y, x2+y2≤2 2. Relevant equations grad f = λ grad g 3. The attempt at a solution to find critical points in the interior region, The partial derivative of f(x,y) with respect to x is 1. The partial derivative of f(x,y) with respect to y is 3. g(x,y) = the constraint = x2+y2≤2, to find critical points on the boundary x2+y2=2 The partial derivative of g(x,y) with respect to x is 2x. The partial derivative of g(x,y) with respect to y is 2y. And normally I would set: 1 = λ 2x and 3 = λ 2y λ = 1/2x and λ = 3/2y so then I would set the equations equal to each other and solve the equation for x and y. What I'm wondering though, Is whether there are actually minimum or maximum values since the partial derivatives of f(x,y) are constants?