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Multivariate Calculus and Optimization

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Below is a file consisting of my study guide for my upcoming exam. I need help with the highlighted Exercises, there is 7 of them.

I repeat I only need the highlighted in yellow Exercises 1-7 solved.

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Solution Summary

The solution gives detailed steps on finding the partial derivatives of some specific two-variable functions. Also, the steps of checking the concave and homogenous properties of the multivariate functions are shown. Finally, a procedure of finding the maximum and minimum values of the functions are explained.