Consider the problem of minimizing
f(x,y) = x2 + 2y2
subject to the constraint g(x,y) = yex2 - 1 = 0.
(A) Solve the constraint equation for y, and then substitute into f(x, y) to obtain a function h(x) of the single variable x. Solve the original minimization problem by minimizing h (round answers to three decimal places).
(B) Confirm your answer by the method of Lagrange multipliers.