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## Critical Point |

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z | overview |

A point is called a critical point of a continuously differentiable function if

gradt

If the second partial derivatives of are continuous at as well,
the type of the critical point can be classified in terms of the eigenvalues of the
Hesse matrix
of .
A critical point is called
- elliptic, if all eigenvalues are different from zero and have the same sign;
- hyperbolic or a saddle point, if there exist eigenvalues with different signs;
- parabolic, if at least one eigenvalue is zero and all nonzero eigenvalues have the same sign.

automatically generated 9/22/2016 |