File:Mittelwertsatz3_c_version.svg · Wikimedia Commons · See Wikimedia Commons
均值定理
Sign in to saveAlso known as Lagrange's mean value theorem, mean value theorems, law of the mean, MVT
数学定理
The mean value theorem states that for any smooth curve between two points, there must be at least one spot on that curve where the tangent line is parallel to the straight line connecting the endpoints. This matters because it's a fundamental tool in mathematics that helps us understand how functions behave and is essential for proving many other important results in calculus.
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Wikidata facts
- Instance of
- theorem
- Part of
- list of theorems
- Image
- Mittelwertsatz3.svg
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- Commons category
- Mean value theorem
- studied by
- calculus
- different from
- Lagrange's theorem
- maintained by WikiProject
- WikiProject Mathematics
- generalization of
- Rolle's theorem
Sources (3)
via Wikidata · CC0
Article · 中文
在數學分析中，均值定理（英語：Mean value theorem）大致是講，給定平面上固定兩端點的可微曲線，則這曲線在這兩端點間至少有一點，在這點該曲線的切線的斜率等於兩端點連結起來的直線的斜率。 更仔細點講，假設函數 在閉區間 連續且在開區間 可微，則存在一點，使得 . 中值定理包括微分中值定理和积分中值定理。
Abstract from DBpedia / Wikipedia · CC BY-SA