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The higher-order derivative test or general derivative test is able to determine whether a function's critical points are maxima, minima, or points of inflection for a wider variety of functions than the second-order derivative test. As shown below, the second-derivative test is mathematically identical to the special case of n = 1 in the ...
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The second derivative test can still be used to analyse critical points by considering the eigenvalues of the Hessian matrix of second partial derivatives of the function at the critical point. If all of the eigenvalues are positive, then the point is a local minimum; if all are negative, it is a local maximum.
At the remaining critical point (0, 0) the second derivative test is insufficient, and one must use higher order tests or other tools to determine the behavior of the function at this point. (In fact, one can show that f takes both positive and negative values in small neighborhoods around (0, 0) and so this point is a saddle point of f.)
The easiest way to create a classification is to use a template if there is one that is appropriate. See the template section below. If there is no template that will work you can add a classification by manually editing a category to insert links. The classification for Contraltos was created with this text:
The Classification Tree Method is a method for test design, [1] as it is used in different areas of software development. [2] It was developed by Grimm and Grochtmann in 1993. [3] Classification Trees in terms of the Classification Tree Method must not be confused with decision trees. The classification tree method consists of two major steps ...
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