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]

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Special case of the mean-value theorem of differential calculus.

It states that if a continuous curve passes through the x-axis twice within a given interval and has a unique tangent line at every point of that interval, then somewhere between the two points of interception it has a tangent parallel to the x-axis.

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Universalium. 2010.

Look at other dictionaries:

  • 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 — 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… …   New Collegiate Dictionary

  • 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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  • Mean value theorem — For the theorem in harmonic function theory, see Harmonic function#Mean value property. Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables …   Wikipedia

  • 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

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