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Rolle's theorem : ウィキペディア英語版 | Rolle's theorem
In calculus, Rolle's theorem essentially states that any real-valued differentiable function that attains equal values at two distinct points must have a stationary point somewhere between them—that is, a point where the first derivative (the slope of the tangent line to the graph of the function) is zero. == Standard version of the theorem ==
If a real-valued function ''f'' is continuous on a proper closed interval (), differentiable on the open interval (''a'', ''b''), and ''f''(''a'') = ''f''(''b''), then there exists at least one ''c'' in the open interval (''a'', ''b'') such that :. This version of Rolle's theorem is used to prove the mean value theorem, of which Rolle's theorem is indeed a special case. It is also the basis for the proof of Taylor's theorem.
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