Chapter 7.4, Problem 30E

Consider the problem of minimizing

     $\begin{array}{ccc}f\left(x,y\right)& =& x^2+2y^2\end{array}$

subject to the constraint $\begin{array}{ccccc}g\left(x,y\right)& =& y{e}^{x^2}-1& =& 0\end{array}$

1. (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).
2. (B) Confirm your answer by the method of Lagrange multipliers.