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- Extreme_value_theorem abstract "In calculus, the extreme value theorem states that if a real-valued function f is continuous in the closed and bounded interval [a,b], then f must attain a maximum and a minimum, each at least once. That is, there exist numbers c and d in [a,b] such that:A related theorem is the boundedness theorem which states that a continuous function f in the closed interval [a,b] is bounded on that interval. That is, there exist real numbers m and M such that:The extreme value theorem enriches the boundedness theorem by saying that not only is the function bounded, but it also attains its least upper bound as its maximum and its greatest lower bound as its minimum.The extreme value theorem is used to prove Rolle's theorem. In a formulation due to Karl Weierstrass, this theorem states that a continuous function from a compact space to a subset of the real numbers attains a maximum and a minimum.".
- Extreme_value_theorem thumbnail Extreme_Value_Theorem.svg?width=300.
- Extreme_value_theorem wikiPageExternalLink ExtremeValueTheorem.
- Extreme_value_theorem wikiPageExternalLink fta_note.shtml.
- Extreme_value_theorem wikiPageExternalLink calc.html.
- Extreme_value_theorem wikiPageID "276881".
- Extreme_value_theorem wikiPageRevisionID "586388862".
- Extreme_value_theorem hasPhotoCollection Extreme_value_theorem.
- Extreme_value_theorem id "6022".
- Extreme_value_theorem id "6023".
- Extreme_value_theorem title "Boundedness Theorem".
- Extreme_value_theorem title "Extreme Value Theorem".
- Extreme_value_theorem urlname "ExtremeValueTheorem".
- Extreme_value_theorem subject Category:Articles_containing_proofs.
- Extreme_value_theorem subject Category:Theorems_in_calculus.
- Extreme_value_theorem subject Category:Theorems_in_real_analysis.
- Extreme_value_theorem type Abstraction100002137.
- Extreme_value_theorem type Communication100033020.
- Extreme_value_theorem type Message106598915.
- Extreme_value_theorem type Proposition106750804.
- Extreme_value_theorem type Statement106722453.
- Extreme_value_theorem type Theorem106752293.
- Extreme_value_theorem type TheoremsInCalculus.
- Extreme_value_theorem type TheoremsInRealAnalysis.
- Extreme_value_theorem comment "In calculus, the extreme value theorem states that if a real-valued function f is continuous in the closed and bounded interval [a,b], then f must attain a maximum and a minimum, each at least once. That is, there exist numbers c and d in [a,b] such that:A related theorem is the boundedness theorem which states that a continuous function f in the closed interval [a,b] is bounded on that interval.".
- Extreme_value_theorem label "Extreme value theorem".
- Extreme_value_theorem label "Extremumstelling".
- Extreme_value_theorem label "Teorema de Weierstrass".
- Extreme_value_theorem label "Teorema de Weierstrass".
- Extreme_value_theorem label "Teorema di Weierstrass".
- Extreme_value_theorem label "Théorème des bornes".
- Extreme_value_theorem label "Теорема Вейерштрасса о функции на компакте".
- Extreme_value_theorem label "最大値最小値定理".
- Extreme_value_theorem label "极值定理".
- Extreme_value_theorem sameAs Weierstrassova_věta.
- Extreme_value_theorem sameAs Teorema_de_Weierstrass.
- Extreme_value_theorem sameAs Théorème_des_bornes.
- Extreme_value_theorem sameAs Teorema_nilai_ekstrem.
- Extreme_value_theorem sameAs Teorema_di_Weierstrass.
- Extreme_value_theorem sameAs 最大値最小値定理.
- Extreme_value_theorem sameAs 최대·최소_정리.
- Extreme_value_theorem sameAs Extremumstelling.
- Extreme_value_theorem sameAs Teorema_de_Weierstrass.
- Extreme_value_theorem sameAs m.01pfkh.
- Extreme_value_theorem sameAs Q752375.
- Extreme_value_theorem sameAs Q752375.
- Extreme_value_theorem sameAs Extreme_value_theorem.
- Extreme_value_theorem wasDerivedFrom Extreme_value_theorem?oldid=586388862.
- Extreme_value_theorem depiction Extreme_Value_Theorem.svg.
- Extreme_value_theorem isPrimaryTopicOf Extreme_value_theorem.