mean value theorem
Word Rarity
Rare
Frequency: Zipf frequency 3.69 in modern English
26
Scrabble Score
16
Letters
5
Syllables
11
Unique Chars
Meaning
name
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.
Example Sentences
- "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."
- "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."
Inflected Forms
the mean value theorem (canonical)
mean value theorems (plural)
Phrases
Cauchy's mean value theorem
extended mean value theorem
Gauss's mean value theorem
intermediate value theorem
Frequently Paired Words
Synonyms
Lagrange's mean value theorem
mean value theorem for derivatives