Word.ws English Dictionary

mean value theorem

mean value theorem proper noun: the theorem that for any real-valued function that is differentiable on an interval, there is a point in that interval where the derivative of the curve equals the slope of the straight line between the graphed function values at the interval's end points.

Proper noun

the mean value theorem

  1. The theorem that for any real-valued function that is differentiable on an interval, there is a point in that interval where the derivative of the curve equals the slope of the straight line between the graphed function values at the interval's end points.
    • for some ζ on the line segment between ̃x and ̌x.1990, A. Neumaier, Interval Methods for Systems of Equations, Cambridge University Press, page 51, In order to get a true bound for the range we may replace the Taylor series in (2) by the mean value...
    • In what follows, we will use the mean value theorem, another one of Lagrange's many contributions to numerical analysis.2003, Sylvain Raynes, Ann Rutledge, The Analysis of Structured Securities, Oxford University Press, page 397
    Synonyms:
    Lagrange's mean value theorem, mean value theorem for derivatives

Noun

mean value theorem (plural mean value theorems)

  1. Any of various theorems that saliently concern mean values.
    • Several mean value theorems in the theory of elasticity have appeared in the recent literature[…].1964, J. H. Bramble, L. E. Payne, Some Mean Value Theorems in Electrostatics: Journal of the Society for Industrial and Applied Mathematics, volume 12, page 105
    • 1984 [Nauka, Moscow], Sergey Ermakov, V. V. Nekrutkin (authors and translators), A. S. Sipin (author), Random Processes for Classical Equations of Mathematical Physics, [1984, С. М. Ермаков, В. В. Некруткин, А. С. Сипин, Случайные процессы для решения классических уравнений математической физики]...

mean value theorem meaning in Tamil and Tagalog

mean value theorem in Tamil

இடைமதிப்புத்தேற்றம், சராசரிப்பெறுமானத்தேற்றம்

mean value theorem in Tagalog

theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope
hunain ng tamtaming halga

Examples of mean value theorem in a sentence

  • The main existence theorems in calculus are the Intermediate Value Theorem, the Extreme Value Theorem, Rolle's Theorem, and the Mean Value Theorem.2007, Denise Szecsei, Calculus, The Career Press, page 10:
  • However, Anton switches, unannounced, to another conceptualization in justifying the Fundamental Theorem - he bases it on the mean value theorem for integrals.1994, Patrick W. Thompson, “Images of Rate and Operational Understanding of the Fundamental Theorem of Calculus”, in Paul Cobb, editor...
  • We prove mean value theorems in the context of integrals which are analogous to the ones studied in Chapter 5.2013, Elimhan Mahmudov, Single Variable Differential and Integral Calculus: Mathematical Analysis, Springer, page 259:
  • The mean value theorem for derivatives provides an important link between the derivative of f on an interval and the behavior of f over the interval.2013, Peter D. Lax, Maria Shea Terrell, Calculus With Applications, Springer, page 171:

Synonyms of mean value theorem

  • Lagrange's mean value theorem
  • mean value theorem for derivatives

Forms of mean value theorem

pluralmean value theorems

Words formed from mean value theorem

  • Cauchy's mean value theorem
  • extended mean value theorem
  • Gauss's mean value theorem

Questions about mean value theorem

What does mean value theorem mean?
Mean value theorem means the theorem that for any real-valued function that is differentiable on an interval, there is a point in that interval where the derivative of the curve equals the slope of the straight line between the graphed function values at the interval's end points.
What is mean value theorem in Tamil?
Mean value theorem in Tamil is இடைமதிப்புத்தேற்றம், சராசரிப்பெறுமானத்தேற்றம். See Mean value theorem meaning in Tamil.
How do you use mean value theorem in a sentence?
The main existence theorems in calculus are the Intermediate Value Theorem, the Extreme Value Theorem, Rolle's Theorem, and the Mean Value Theorem.
What part of speech is mean value theorem?
Mean value theorem can be a proper noun or a noun.

Words near mean value theorem in the dictionary

  1. mean time
  2. mean time to failure
  3. mean times
  4. mean to
  5. mean to say
  6. mean value theorem
  7. mean value theorems
  8. mean well
  9. mean white
  10. mean whites
  11. mean world syndrome

Source and license

Adapted from Wiktionary: mean value theorem (page history and authors); mean value theorem (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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Cite this entry: “mean value theorem.” Word.ws, https://word.ws/mean_value_theorem. Based on Wiktionary, CC BY-SA 4.0.