Question

Use the method of Lagrange Multipliers to determine the max and min of f(x,y)=2x-3y subject to the constraint g(x,y)=4-(x^2)-2y=0

Answer 1

I have attached what I have done so far. How do I tell if -(20/3) is a min or max? And is there another solution that may be a min or max or is this the only solution? Thanks