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| {{unreferenced|date=September 2012}}
| | Hi there, I am Alyson Pomerleau and I think it sounds quite good when you say it. She works as a journey agent but quickly she'll be on her personal. To perform lacross is some thing he would by no means give up. I've always loved living in Alaska.<br><br>Here is my page - [http://www.edmposts.com/build-a-beautiful-organic-garden-using-these-ideas/ free psychic readings] |
| In [[mathematics]], the '''higher-order derivative test''' is used to find maxima, minima, and points of inflection for sufficiently differentiable real-valued functions.
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| ==The general derivative test for stationary points==
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| Let <math>f</math> be a real-valued, sufficient [[differentiable function]] on the interval <math>I \subset \R, \; c \in I</math> and <math>n \ge 1</math> an integer. If now holds
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| <math>f'(c)=\cdots=f^{(n)}(c)=0\quad \text{and}\quad f^{(n+1)}(c)\,\not= 0</math> | |
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| then, either
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| ''n'' is odd and we have a local extremum at ''c''. More precisely:
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| #<math>f^{(n+1)}(c)<0 \Rightarrow c</math> is a point of a maximum
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| #<math>f^{(n+1)}(c)>0 \Rightarrow c</math> is a point of a minimum
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| or
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| ''n'' is even and we have a (local) saddle point at ''c''. More precisely:
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| #<math>f^{(n+1)}(c)<0 \Rightarrow c</math> is a strictly decreasing point of inflection
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| #<math>f^{(n+1)}(c)>0 \Rightarrow c</math> is a strictly increasing point of inflection
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| .
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| This analytical test classifies any stationary point of <math>f</math>.
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| ==See also==
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| *[[Extremum]]
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| *[[First derivative test]]
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| *[[Second derivative test]]
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| *[[Hessian_matrix#Second_derivative_test]]
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| *[[Saddle point]]
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| *[[Inflection point]]
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| *[[Stationary point]]
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| [[Category:Calculus]]
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| {{mathanalysis-stub}}
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Latest revision as of 14:25, 6 January 2015
Hi there, I am Alyson Pomerleau and I think it sounds quite good when you say it. She works as a journey agent but quickly she'll be on her personal. To perform lacross is some thing he would by no means give up. I've always loved living in Alaska.
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