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.

CITE THIS AS:

Weisstein, Eric W. "Saddle Point." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SaddlePoint.html