Saddle point determination Graphical method etc Components

A point of a function or surface which is a stationary point but not an extremum. An example of a one-dimensional function with a saddle point is f(x)=x^3, which has

f^'(x)	=	3x^2	
(1)
f^('')(x)	=	6x	
(2)
f^(''')(x)	=	6.	
(3)

This function has a saddle point at x_0=0 by the extremum test since f^('')(x_0)=0 and f^(''')(x_0)=6!=0. Surfaces can also have saddle points, which the second derivative test can sometimes be used to identify. Examples of surfaces with a saddle point include the handkerchief surface and monkey saddle.