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Mean value theorem

In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating that the average rate of change of such a function over an interval is equal to the instantaneous rate of change at some point in the interval. For example, if a car smoothly travels a certain distance over…

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Cauchy's mean value theorem

Mean value theorem in several variables

Mean value theorem for vector-valued functions

Mean value theorems for definite integrals

Generalizations

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Mean value theorem

Nodes60
Edges59
Triples76
Avg. degree1.97
Density0.033333
Components1

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Mean value theorem

Top relations

related to External links · 15
Mean value theorem → Cauchy, Cauchy's Mean-Value Theorem, Derivative, Differential Calculus, EMS Press, Encyclopedia, Eric, Khan Academy, Mathematics, MathWorld, Mean, Mean-Value Theorem, PlanetMath, Unit, Weisstein
related to history · 12
Mean value theorem → Astronomy, Augustin Louis Cauchy, Bhāskara II, Govindasvāmi, India, Kerala School, Many, Mathematics, Michel Rolle, Parameshvara, Rolle's, The
related to Mean value inequality · 12
Mean value theorem → Analysis, Foundations, Henstock, If, In, Jean Dieudonné, Kurzweil, Modern Analysis, Rm, Rn, Serge Lang, The
related to Proof · 8
Mean value theorem → Cauchy's, Define, Namely, Rolle's, Since, The, Thus, We
related to Implications · 6
Mean value theorem → Assume, By, If, Let, Proof, Theorem
related to Mean value theorem for vector-valued functions · 4
Mean value theorem → For, However, Theorem, There
related to Mean value theorem in several variables · 4
Mean value theorem → Fix, Let, Since, The
related to Statement · 4
Mean value theorem → Let, Rolle's, The, Then
related to Cauchy's mean value theorem · 3
Mean value theorem → Cauchy's, It, Of
related to Second mean value theorem for definite integrals · 3
Mean value theorem → Here, Note, There

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displaystyle theorem value mean differentiable function continuous interval point derivative since exists one functions f' proof constant open given line

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SubjectPredicateObjectConfidenceSrc
Mean value theoremis ageneralization of Rolle's theorem0.90text
Mean value theoremis aspecial case of Cauchy's mean value theorem when g0.90text
Mean value theoremrelated to Cases where the theorem cannot be appliedAll0.60section
Mean value theoremrelated to Cauchy's mean value theoremCauchy's0.60section
Mean value theoremrelated to Cauchy's mean value theoremIt0.60section
Mean value theoremrelated to Cauchy's mean value theoremOf0.60section
Mean value theoremrelated to External linksCauchy0.60section
Mean value theoremrelated to External linksEncyclopedia0.60section
Mean value theoremrelated to External linksMathematics0.60section
Mean value theoremrelated to External linksEMS Press0.60section
Mean value theoremrelated to External linksMean0.60section
Mean value theoremrelated to External linksPlanetMath0.60section

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