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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 Intermediate value theorem ： ウィキペディア英語版 Intermediate value theorem In mathematical analysis, the intermediate value theorem states that if a continuous function ''f'' with an interval (''b'' ) as its domain takes values ''f''(''a'') and ''f''(''b'') at each end of the interval, then it also takes any value between ''f''(''a'') and ''f''(''b'') at some point within the interval. This has two important specializations: 1) If a continuous function has values of opposite sign inside an interval, then it has a root in that interval (Bolzano's theorem). 2) The image of a continuous function over an interval is itself an interval. ==Motivation== This captures an intuitive property of continuous functions: given ''f'' continuous on (2 ) with the known values ''f''(1) = 3 and ''f''(2) = 5. Then the graph of ''y'' = ''f''(''x'') must pass through the horizontal line ''y'' = 4 while ''x'' moves from 1 to 2. It represents the idea that the graph of a continuous function on a closed interval can be drawn without lifting your pencil from the paper. 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「Intermediate value theorem」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.