The second partial derivative test classifies a critical point 
of a twice continuously differentiable function 
. Define
 |
If 
and 
, the point is a local minimum;
if 
and 
, it is a local maximum.
If 
, the point is a saddle
point. When 
,
the test is inconclusive. These cases are the two-dimensional form of classifying
the Hessian by its definiteness.
