Rolle's theoremn.

Brit.

/ˈrɒlz ˌθɪərəm/, U.S.

/ˈrɑlz ˌθiərəm/,

/ˈrɑlz ˌθɪrəm/

Forms:

α. 1800s– Rolle's theorem.

β. 1900s– Rolle theorem.

Origin: From a proper name, combined with an English element; modelled on a German lexical item. Etymons: proper name Rolle , theorem n..

Etymology: In α. forms < the genitive of the name of Michel Rolle (1652–1719), French mathematician + theorem n., after German Rolle's Satz ( M. W. Drobisch Grundzüge der Lehre von den höheren numerischen Gleichungen (1834) p. xxvi). In β. forms < the name of Michel Rolle + theorem n.

Mathematics.

A theorem in analysis stating that if a differentiable function has the same value at two different points, there is at least one point situated between them for which the derivative of the function is equal to zero.Rolle's theorem is a special case of the mean-value theorem.

ΚΠ

1858 J. Hymers Treat. Theory Algebraical Equations (ed. 3) Contents p. iv Rolle's theorem:—An odd number of the roots of f′(x) = 0 lies between each adjacent two of the roots of f(x) = 0; and if they are known, the number and situation of the roots of f(x) = 0 can be found.

1918 Ann. Math. 19 252 By a corollary of Rolle's Theorem the derived equation of (1) has at least r −1 positive roots.

1983 Trans. Amer. Math. Soc. 277 797 We apply the Rolle theorem m + 1 times and obtain n + m + 1 as an upper bound on the number of zeros.

2006 D. A. Brannan First Course Math. Anal. vi. 233 We now generalise Rolle's Theorem and assert that there is always a point where the tangent to the graph is parallel to the chord joining the end-points.

This is a new entry (OED Third Edition, November 2010; most recently modified version published online March 2022).

单词	rolles theorem
释义	Rolle's theoremn. Brit. /ˈrɒlz ˌθɪərəm/, U.S. /ˈrɑlz ˌθiərəm/, /ˈrɑlz ˌθɪrəm/ Forms: α. 1800s– Rolle's theorem. β. 1900s– Rolle theorem. Origin: From a proper name, combined with an English element; modelled on a German lexical item. Etymons: proper name Rolle , theorem n.. Etymology: In α. forms < the genitive of the name of Michel Rolle (1652–1719), French mathematician + theorem n., after German Rolle's Satz ( M. W. Drobisch Grundzüge der Lehre von den höheren numerischen Gleichungen (1834) p. xxvi). In β. forms < the name of Michel Rolle + theorem n. Mathematics. A theorem in analysis stating that if a differentiable function has the same value at two different points, there is at least one point situated between them for which the derivative of the function is equal to zero.Rolle's theorem is a special case of the mean-value theorem. ΚΠ 1858 J. Hymers Treat. Theory Algebraical Equations (ed. 3) Contents p. iv Rolle's theorem:—An odd number of the roots of f′(x) = 0 lies between each adjacent two of the roots of f(x) = 0; and if they are known, the number and situation of the roots of f(x) = 0 can be found. 1918 Ann. Math. 19 252 By a corollary of Rolle's Theorem the derived equation of (1) has at least r −1 positive roots. 1983 Trans. Amer. Math. Soc. 277 797 We apply the Rolle theorem m + 1 times and obtain n + m + 1 as an upper bound on the number of zeros. 2006 D. A. Brannan First Course Math. Anal. vi. 233 We now generalise Rolle's Theorem and assert that there is always a point where the tangent to the graph is parallel to the chord joining the end-points. This is a new entry (OED Third Edition, November 2010; most recently modified version published online March 2022). < n.1858
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