relations between Hessian matrix and local extrema
If is negative definite (http://planetmath.org/NegativeDefinite), then is a strict local maximum for .
Let the neighborhood of be in the domain for , and let have continuous partial derivatives of first and second order. Let . If , then is a strict local minimum. If , then is a strict local maximum. In the case that , being , is said to be an inflexion point (also called turning point). A typical example is , , , , , .
|Title||relations between Hessian matrix and local extrema|
|Date of creation||2013-03-22 12:59:52|
|Last modified on||2013-03-22 12:59:52|
|Last modified by||bshanks (153)|
|Defines||second derivative test|