Show that the Lagrange equations for (x, y) = 2x + y subject to the constraint g(x, y) = x 2 y 2 =

Show that the Lagrange equations for ƒ(x, y) = 2x + y subject to the constraint g(x, y) = x² − y² = 1 have a solution but that f has no min or max on the constraint curve. Does this contradict Theorem 1?

THEOREM 1 Lagrange Multipliers Assume that f(x, y) and g(x, y) are differen- tiable functions. If f(x, y) has a local minimum or a local maximum on the constraint curve g(x, y) = 0 at P = (a, b), and if Vgp #0, then there is a scalar such that Vfp = Vgp