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Darboux's theorem (analysis) : ウィキペディア英語版 | Darboux's theorem (analysis) Darboux's theorem is a theorem in real analysis, named after Jean Gaston Darboux. It states that all functions that result from the differentiation of other functions have the intermediate value property: the image of an interval is also an interval. When ''f'' is continuously differentiable (''f'' in ''C''1(())), this is a consequence of the intermediate value theorem. But even when ''f′'' is ''not'' continuous, Darboux's theorem places a severe restriction on what it can be. ==Darboux's theorem== Let be an open interval, a real-valued differentiable function. Then has the intermediate value property: If and are points in with 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「Darboux's theorem (analysis)」の詳細全文を読む
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