Question: How to find out intervals of a variables where function is monotonically increasing?

Hello Everyone,


I have been working on a multi variable expression. I would like to have the intervals where the function is monotonically increasing. I am trying to study any available method for multivariable expressions.

I came across various papers and sites which are explicitly mentioned single variable equations. finding out the critical points and studying the sign of the first derivative. Same cannot be applied for the multi variable expression.

above link explain for single variable functions. I would be grateful if someone could explain me a method or idea  which helps me out in solving for multivariable functions


Thanks a lot in advance

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