1. The problem statement, all variables and given/known data Lagrange multipliers to find the maximum and minimum values of f(x,y) = 4x^3 + y^2 subject to the constraint 2x^2 + y^2 = 1. Find points of these extremum. 2. Relevant equations 3. The attempt at a solution g(x,y)= 2x^2 + y^2 - 1 f(x,y)= 4x^3 + y^2 Gradient F= 12x^2i + 24yj Gradient G= 4xi + 2yj Gradient = 4x^3 + y^2 - λ(2x^2 + y^2 - 1) = [12x^2- λ4x, 2y - 2λy, -2x^2 - y^2 - 1] 12x^2 - λ4x = 0 3x = λ 2y - 2λy = 0 λ= 1 x = 1/3 (Is this correct?) fx (x,y) = 12x^2 x=0 fy (x,y) = 2y y=0 No minima or maxima is my conclusion but I'm very sure it's wrong. Also is the 3-D representation somewhat like a paraboloid with a ellipsoid constraint? Thanks!