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.
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saddle point
