How to prove a function of multiple variables is increasing

[udit]

How do I prove that a function of multiple variables e.g. f(x1,x2,x3,....,xn) is non decreasing. For single variable we prove that the first derivative is > 0, How do I do it for multiple variables? Check for non negativity of partial derivatives.

thanks

 

[zorro]

Hi udit,

You should define what means "non decreasing" in the case of a function of multiple variables. If you mean that is non decreasing with respect to each variable when all the other are fixed, then what you said (check for non negativity of partial derivatives) is right.
In general. you could analyze the behaviour across a line, not necessarily "parallel" to the axis.
Regards

Z