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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Fermat's theorem (stationary points) ： ウィキペディア英語版 Fermat's theorem (stationary points) In mathematics, Fermat's theorem (also known as Interior extremum theorem) is a method to find local maxima and minima of differentiable functions on open sets by showing that every local extremum of the function is a stationary point (the function derivative is zero in that point). Fermat's theorem is a theorem in real analysis, named after Pierre de Fermat. By using Fermat's theorem, the potential extrema of a function $\backslash displaystyle\; f$, with derivative $\backslash displaystyle\; f\text{'}$, are found by solving an equation in $\backslash displaystyle\; f\text{'}$. Fermat's theorem gives only a necessary condition for extreme function values, and some stationary points are inflection points (not a maximum or minimum). The function's second derivative, if it exists, can determine if any stationary point is a maximum, minimum, or inflection point. ==Statement== One way to state Fermat's theorem is that whenever you compute the derivative of a function's local extrema, the result will always be zero. In precise mathematical language: :Let $f\backslash colon\; (a,b)\; \backslash rightarrow\; \backslash mathbb$ be a function and suppose that $\backslash displaystyle\; x\_0\; \backslash in\; (a,b)$ is a local extremum of $\backslash displaystyle\; f$. If $\backslash displaystyle\; f$ is differentiable at $\backslash displaystyle\; x\_0$, then $\backslash displaystyle\; f\text{'}(x\_0)\; =\; 0$. Another way to understand the theorem is via the contrapositive statement. If the derivative of a function at any point is not zero, that point is not an extrema. Formally: :If $\backslash displaystyle\; f$ is differentiable at $\backslash displaystyle\; x\_0\; \backslash in\; (a,b)$, and $\backslash displaystyle\; f\text{'}(x\_0)\; \backslash neq\; 0$, then $x\_0$ is not a local extremum of ''f.'' 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fermat's theorem (stationary points)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.