Finding extreme values of a multivariable function

The general idea is analogous to single variable functions. Whether we are discussing the function's domain or a subdomain of it, we have to use derivatives to analyse how the function behaves to know whether a point is a maximum or a minimum. For two variables the idea is the same as for one variable, in a certain interval the function ca be constant, crescent or decrescent. For three and more variables we lose the function's graph, but the algebra is the same.