Meaning of mean value theorem | Babel Free

Definitions

1. Any of various theorems that saliently concern mean values.
2. 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.
   uncountable

Equivalents

Examples

“Several mean value theorems in the theory of elasticity have appeared in the recent literature[…].”

“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.”

“However, Anton switches, unannounced, to another conceptualization in justifying the Fundamental Theorem - he bases it on the mean value theorem for integrals.”

“We prove mean value theorems in the context of integrals which are analogous to the ones studied in Chapter 5.”

“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.”

“for some ζ on the line segment between ̃x and ̌x.”

“In what follows, we will use the mean value theorem, another one of Lagrange's many contributions to numerical analysis.”

“The main existence theorems in calculus are the Intermediate Value Theorem, the Extreme Value Theorem, Rolle's Theorem, and the Mean Value Theorem.”

CEFR level