Dictionary
Words, grammatical forms and meanings linked to the ontology.
mean value theorem en · NOUN
Meanings
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Any of various theorems that saliently concern mean values.
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], 1989, Kluwer, Softcover Reprint, page xiii,
For parabolic equations (Section 5.1) and for the exterior Dirichlet problem (Section 5.2), it is possible to apply the well known mean value theorems.
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: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, Learning Mathematics, Kluwer, page 167: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:
Forms
Deriveds
Gauss's mean value theorem · Cauchy's mean value theorem · extended mean value theorem
Relateds
intermediate value theorem
mean value theorem en · PROPN
Meanings
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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.
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: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: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 theorem, which tells us that f(̃x)=f(̌x)+f'(ζ)(̃x-̌x)
Forms
Synonyms
Lagrange's mean value theorem · mean value theorem for derivatives
Translations (17)
bg теорема за средните стойности (theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope) · fi väliarvolause (theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope) · he משפט לגראנז׳ (theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope) · de Mittelwertsatz (theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope) · fi differentiaalilaskennan väliarvolause (theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope) · cmn 中值定理 (theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope) · fr théorème des accroissements finis (theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope) · tl hunain ng tamtaming halga (theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope) · gl teorema del valor medio (theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope) · it teorema dell'incremento finito (theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope) · es teorema del valor medio (theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope) · it teorema di Lagrange (theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope) · ca teorema del valor mitjà (theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope) · ast teorema del valor medu (theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope) · pt teorema do valor médio (theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope) · he משפט הערך הממוצע (theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope) · it teorema del valor medio (theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope)