Word Count : 137

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Consider the function (f(x,y)=xy) subject to the constraint [ g(x,y)=\frac{x^{2}}{8}+\frac{y^{2}}{2}-1=0. ] Using Lagrange multipliers, we solve [ \nabla f=\lambda \nabla g. ] Thus, [ (y,x)=\lambda\left(\frac{x}{4},y\right), ] which _________ ___ _____ ___ __________ ______ _____ _______ ________ _________ ____.
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