Question: Lagrange multipliers to find the indicated extrema of f subject to two constraints. In each case assume that x, y and z are nonnegative.

Maximize: \(f\left( x,y,\lambda \right)={{x}^{2}}+{{\left( y-10 \right)}^{2}}\)

Constraints: \(L\left( x,y,\lambda \right)={{\left( x-4 \right)}^{2}}+{{y}^{2}}=4\)