My first post and I am new to forum etiquette, please go easy on me.(adsbygoogle = window.adsbygoogle || []).push({});

I have an exam in a few days and have a good grasp on the content. Historically the professor has been putting harder Lagrange questions on the exam than are available in my textbook and supplement books or that I can find similar ones of online. I have looked for 2 hours last night and another 3 today at 30 different explanations of Lagrange with constraints and I cannot find any as difficult as these to help guide me.. I am not lazy..any advice or simply point me in the right direction on solving these would be appreciated...I particularly have an issue looking for methods of solving the resulting systems of partial derivative equations. Thank you for any help in advance.

Type 1

Absolute Maximum and minimum of f(x,y,z) = x^2 + y^2 + z^2 - xyz

constrained by x^2 + y^2 + z^2 <= 1

Type 2

Maximum and minimum of f(x,y,z) = x^2 + y^2 - z^2 - x -y - z

in the region 0 <= x^2 + y^2 <= z^2 <= 4

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# Advanced Lagrange Maxima Minima Problems

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