How to study the behavior of a vector valued function?

[maCrobo]

Hi, I would like to know how to treat a vector valued function when I want to know where are minima, maxima and saddle points.

Thanks in advance!

 

[Muphrid]

Perhaps there is some way to consider such properties, but to me, such concepts no longer have meaning. How could you say a vector has a minimum or maximum value in a region or neighborhood? You could consider the magnitude, but that's a scalar function and requires no more thought than scalar function theory that you're already familiar with.