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- Mean_value_theorem abstract "In mathematics, the mean value theorem states, roughly: that given a 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. The theorem is used to prove global statements about a function on an interval starting from local hypotheses about derivatives at points of the interval.More precisely, if a function f is continuous on the closed interval [a, b], where a < b, and differentiable on the open interval (a, b), then there exists a point c in (a, b) such thatA special case of this theorem was first described by Parameshvara (1370–1460) from the Kerala school of astronomy and mathematics in his commentaries on Govindasvāmi and Bhaskara II. The mean value theorem in its modern form was later stated by Augustin Louis Cauchy (1789–1857). It is one of the most important results in differential calculus, as well as one of the most important theorems in mathematical analysis, and is useful in proving the fundamental theorem of calculus. The mean value theorem follows from the more specific statement of Rolle's theorem, and can be used to prove the more general statement of Taylor's theorem (with Lagrange form of the remainder term).".
- Mean_value_theorem thumbnail Mvt2.svg?width=300.
- Mean_value_theorem wikiPageExternalLink MeanValueTheorem.html.
- Mean_value_theorem wikiPageExternalLink mean-value-theorem.
- Mean_value_theorem wikiPageID "19662".
- Mean_value_theorem wikiPageRevisionID "603711862".
- Mean_value_theorem hasPhotoCollection Mean_value_theorem.
- Mean_value_theorem id "p/c020990".
- Mean_value_theorem title "Cauchy theorem".
- Mean_value_theorem subject Category:Articles_containing_proofs.
- Mean_value_theorem subject Category:Theorems_in_calculus.
- Mean_value_theorem subject Category:Theorems_in_real_analysis.
- Mean_value_theorem type Abstraction100002137.
- Mean_value_theorem type Communication100033020.
- Mean_value_theorem type Message106598915.
- Mean_value_theorem type Proposition106750804.
- Mean_value_theorem type Statement106722453.
- Mean_value_theorem type Theorem106752293.
- Mean_value_theorem type TheoremsInCalculus.
- Mean_value_theorem type TheoremsInRealAnalysis.
- Mean_value_theorem comment "In mathematics, the mean value theorem states, roughly: that given a 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.".
- Mean_value_theorem label "Mean value theorem".
- Mean_value_theorem label "Middelwaardestelling".
- Mean_value_theorem label "Mittelwertsatz der Differentialrechnung".
- Mean_value_theorem label "Teorema del valor medio".
- Mean_value_theorem label "Teorema di Lagrange".
- Mean_value_theorem label "Teorema do valor médio".
- Mean_value_theorem label "Théorème des accroissements finis".
- Mean_value_theorem label "Twierdzenie Lagrange'a (rachunek różniczkowy)".
- Mean_value_theorem label "Формула конечных приращений".
- Mean_value_theorem label "مبرهنة القيمة الوسطى".
- Mean_value_theorem label "中值定理".
- Mean_value_theorem label "平均値の定理".
- Mean_value_theorem sameAs Věta_o_střední_hodnotě_diferenciálního_počtu.
- Mean_value_theorem sameAs Mittelwertsatz_der_Differentialrechnung.
- Mean_value_theorem sameAs Θεώρημα_μέσης_τιμής.
- Mean_value_theorem sameAs Teorema_del_valor_medio.
- Mean_value_theorem sameAs Batez_besteko_balioaren_teorema.
- Mean_value_theorem sameAs Théorème_des_accroissements_finis.
- Mean_value_theorem sameAs Teorema_nilai_purata.
- Mean_value_theorem sameAs Teorema_di_Lagrange.
- Mean_value_theorem sameAs 平均値の定理.
- Mean_value_theorem sameAs 평균값_정리.
- Mean_value_theorem sameAs Middelwaardestelling.
- Mean_value_theorem sameAs Twierdzenie_Lagrange'a_(rachunek_różniczkowy).
- Mean_value_theorem sameAs Teorema_do_valor_médio.
- Mean_value_theorem sameAs m.04z79.
- Mean_value_theorem sameAs Q189136.
- Mean_value_theorem sameAs Q189136.
- Mean_value_theorem sameAs Mean_value_theorem.
- Mean_value_theorem wasDerivedFrom Mean_value_theorem?oldid=603711862.
- Mean_value_theorem depiction Mvt2.svg.
- Mean_value_theorem isPrimaryTopicOf Mean_value_theorem.