mean value theorem
Language: English
Part of speech: noun
Forms: form: mean value theorems
Senses: examples: text: Several mean value theorems in the theory of elasticity have appeared in the recent literature[…].
ref: 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:
text: 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.
text: However, Anton switches, unannounced, to another conceptualization in justifying the Fundamental Theorem - he bases it on the mean value theorem for integrals.
ref: 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:
text: We prove mean value theorems in the context of integrals which are analogous to the ones studied in Chapter 5.
ref: 2013, Elimhan Mahmudov, Single Variable Differential and Integral Calculus: Mathematical Analysis, Springer, page 259:
text: 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.
ref: 2013, Peter D. Lax, Maria Shea Terrell, Calculus With Applications, Springer, page 171:
topics: mathematics
sciences
glosses: Any of various theorems that saliently concern mean values.
examples: text: for some ζ on the line segment between ̃x and ̌x.
ref: 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)
text: In what follows, we will use the mean value theorem, another one of Lagrange's many contributions to numerical analysis.
ref: 2003, Sylvain Raynes, Ann Rutledge, The Analysis of Structured Securities, Oxford University Press, page 397:
text: The main existence theorems in calculus are the Intermediate Value Theorem, the Extreme Value Theorem, Rolle's Theorem, and the Mean Value Theorem.
ref: 2007, Denise Szecsei, Calculus, The Career Press, page 10:
topics: calculus
mathematics
sciences
glosses: 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.
Synonyms: sense: theorem that a point exists where the derivative equals the overall slope
word: Lagrange mean value theorem
sense: theorem that a point exists where the derivative equals the overall slope
word: mean value theorem for derivative
Derived terms: Cauchy's mean value theorem
extended mean value theorem
Gauss's mean value theorem
Related terms: intermediate value theorem