1. The problem statement, all variables and given/known data Consider the intersection of the elliptic paraboloid Z = X2+4Y2 , and the cylinder X2+Y2= 1. Use Lagrange multipliers to find the highest, and lowest points on the curve of intersection. 2. Relevant equations The gradient equations of both functions. 3. The attempt at a solution I have ∇f= <2X, 8Y> and ∇g= <2X, 2Y>. the constraint equation is X2+Y2 = 1. I set the equations equal to get: 2X = (2X)λ 8Y = (2Y)λ When I try to solve it always removes the variable. Where do I go from here to solve?