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Mean value theorem — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Mean_value_theorem
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-31T10:04:09.215Z
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Mean value theorem — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Mean_value_theorem (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_4ff64637d751 (Metraipolis archive dc_4ff64637d751, sha256 347f6423a05da4736706f9dfee5f7c41330fc34ec26044bf68b027746a3a863c)

BibTeX

@misc{dc4ff64637d751,
  title = {Mean value theorem — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Mean_value_theorem},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_4ff64637d751; sha256 347f6423a05da4736706f9dfee5f7c41330fc34ec26044bf68b027746a3a863c},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Mean_value_theorem. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating that the average rate of change of such a function over an interval is equal to the instantaneous rate of change at some point in the interval. For example, if a car smoothly travels a certain distance over a given finite time interval, then at some moment during the trip, its instantaneous speed equals its average speed for the whole trip. The theorem states precisely that if a real-valued function is continuous on a closed interval [ a , b ] {\displaystyle [a,b]} , with a < b {\displaystyle a<b} , and differentiable on the interior ( a , b ) {\displaystyle (a,b)} , then there is at least one point in ( a , b ) {\displaystyle (a,b)} where the derivative equals the function's average rate of change over the whole interval. Geometrically, this means that at some point the tangent to the graph is parallel to the secant line through the interval's endpoints. It is used in proving other general properties of differentiable functions.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «linear algebra»).
Fonte: Wikipedia in inglese, voce «Mean value theorem» — https://en.wikipedia.org/wiki/Mean_value_theorem
Wikidata Q189136: «teorema matematico» (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q189136
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Mean_value_theorem?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1381690119, consultata il 2026-10-31T09:47:29.145Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 18dd09a20bd6b5ea7066ecb40391aee4c24b5eb4c1272b393a7d73cb67430e0f