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Mean value theorem - Wikipedia

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In mathematics, the mean value theorem (or Lagrange theorem) states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints. It is one of the most important results in real analysis. This theorem is used to prove statements about a function on an interval starting from local hypotheses about derivatives at points of the interval. More precisely, the theorem states that if 𝑓 is a continuous function on the closed interval [ 𝑎 , 𝑏 ] and differentiable on the open interval ( 𝑎 , 𝑏 ) , then there exists a point 𝑐 in ( 𝑎 , 𝑏 ) such that the tangent at 𝑐 is parallel to the secant line through the endpoints ( 𝑎 , 𝑓 ( 𝑎 ) ) and ( 𝑏 , 𝑓 ( 𝑏 ) ) , that is, A special case of this theorem for inverse interpolation of the sine was first described by Parameshvara (1380–1460), from the Kerala School of Astronomy and Mathematics in India, in his commentaries on

Mean value theorem - Wikipedia Jump to content From Wikipedia, the free encyclopedia Theorem in mathematics For the theorem in harmonic function theory, see Harmonic function § The mean value property . For the unsolved problem in complex analysis, see Mean value problem . Part of a series of articles about Calculus ∫ a b f ′ ( t ) d t = f ( b ) − f ( a ) {\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)} Fundamental theorem Limits Continuity Rolle's theorem Mean value theorem Inverse function theorem Differential Definitions Derivative ( generalizations ) Differential infinitesimal of a functio

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