[See Solution] Use Lagrange multipliers to find the indicated extrema Maximize f(x,y,z)=xyz , s.t. x^2+z^2=5 , x-2y=0
Question: Use Lagrange multipliers to find the indicated extrema
\[\begin{aligned} & \text{Maximize}\,\,\,\,\,f\left( x,y,z \right)=xyz \\ & \text{s}\text{.t}\text{.}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}^{2}}+{{z}^{2}}=5 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x-2y=0 \\ \end{aligned}\]
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