# Rolle's theorem

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Rolle's theorem
noun Etymology: Michel Rolle died 1719 French mathematician Date: circa 1891 a theorem in mathematics: if a curve is continuous, crosses the x-axis at two points, and has a tangent at every point between the two intercepts, its tangent is parallel to the x-axis at some point between the intercepts

New Collegiate Dictionary. 2001.

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• Rolle's theorem — In calculus, a branch of mathematics, Rolle s theorem essentially states that a differentiable function, which attains equal values at two points, must have a stationary point somewhere between them.tandard version of the theoremIf a real valued… …   Wikipedia

• rolle's theorem — ˈrȯlz , ˈrōlz noun Usage: usually capitalized R Etymology: after Michel Rolle died 1719 French mathematician : a theorem in mathematics: if a curve is continuous, crosses the x axis at two points, and has a single tangent at every point between… …   Useful english dictionary

• Rolle's theorem — /rohlz/, Math. the theorem that a differentiable function having equal values at the endpoints of an interval has a derivative equal to zero at some point in the interval. [1890 95; named after Michel Rolle (d. 1719), French mathematician] * * *… …   Universalium

• Rolle'stheorem — Rolle s theorem (rôlz, rōlz) n. A theorem stating that if a curve is continuous, has two x intercepts, and has a tangent at every point between the intercepts, at least one of these tangents is parallel to the x axis.   [After MichelRolle (1652… …   Universalium

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• Michel Rolle — (April 21, 1652 – November 8, 1719) was a French mathematician. He is best known for Rolle s theorem (1691), and he deserves to be known as the co inventor in Europe of Gaussian elimination (1690). Contents 1 Life 2 Work 3 Critique of… …   Wikipedia

• Gauss-Lucas theorem — In complex analysis, the Gauss Lucas theorem gives a geometrical relation between the roots of a polynomial P and the roots of its derivative P . The set of roots of a real or complex polynomial is a set of points in the complex plane. The… …   Wikipedia