Question Number 131690 by LYKA last updated on 07/Feb/21
![use the method of lagrange multipliers to fond the extrema of f(x.y.z)=24x^2 y^2 (6−z^2 ) subject to z=x^2 +y^2 −2xy](https://www.tinkutara.com/question/Q131690.png)
$${use}\:{the}\:{method}\:{of}\: \\ $$$$\boldsymbol{{lagrange}}\:\boldsymbol{{multipliers}}\:\boldsymbol{{to}}\:\boldsymbol{{fond}}\: \\ $$$$\boldsymbol{{the}}\:\boldsymbol{{extrema}}\:\boldsymbol{{of}}\: \\ $$$$\boldsymbol{{f}}\left(\boldsymbol{{x}}.\boldsymbol{{y}}.\boldsymbol{{z}}\right)=\mathrm{24}\boldsymbol{{x}}^{\mathrm{2}} \boldsymbol{{y}}^{\mathrm{2}} \left(\mathrm{6}−\boldsymbol{{z}}^{\mathrm{2}} \right) \\ $$$$\boldsymbol{{subject}}\:\boldsymbol{{to}}\:\boldsymbol{{z}}=\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{{xy}} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$