Saddle Point

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 , which has

			(1)
			(2)
			(3)

This function has a saddle point at  by the extremum test since  and .

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.