Applications of the Taylor Series

In the present lesson a few applications of the Taylor series for functions \(f: \mathbb {R}^n \rightarrow \mathbb {R}\) will be discussed. The analysis is limited to functions of two or three variables. The first application deals with the search for the extreme and saddle points of a surface given by means of implicit (e.g., \(f(x,y,z) = \text {constant}\) ) or explicit (e.g., \(z = z(x,y)\) ) relations.