About: Darboux's theorem (analysis)

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In mathematics, Darboux's theorem is a theorem in real analysis, named after Jean Gaston Darboux. It states that every function that results from the differentiation of another function has the intermediate value property: the image of an interval is also an interval. When ƒ is continuously differentiable (ƒ in C1([a,b])), this is a consequence of the intermediate value theorem. But even when ƒ′ is not continuous, Darboux's theorem places a severe restriction on what it can be.

Attributes	Values
rdfs:label	Darboux's theorem (analysis) (en)
rdfs:comment	In mathematics, Darboux's theorem is a theorem in real analysis, named after Jean Gaston Darboux. It states that every function that results from the differentiation of another function has the intermediate value property: the image of an interval is also an interval. When ƒ is continuously differentiable (ƒ in C1([a,b])), this is a consequence of the intermediate value theorem. But even when ƒ′ is not continuous, Darboux's theorem places a severe restriction on what it can be. (en)
sameAs	Darboux's theorem (analysis) Darboux's theorem (analysis)
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:Short_description dbt:SpringerEOM dbt:PlanetMath_attribution
Subject	Articles containing proofs Continuous mappings Theorems in calculus Theorems in real analysis
gold:hypernym	Theorem
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Darboux's_theorem_(analysis)?oldid=1041456151&ns=0
Wikipage page ID	4130888 (xsd:integer)
page length (characters) of wiki page	6964 (xsd:nonNegativeInteger)
Wikipage revision ID	1041456151 (xsd:integer)
Link from a Wikipage to another Wikipage	Nowhere continuous function Articles containing proofs Continuous mappings Theorems in calculus Differentiable function Jean Gaston Darboux Classification of discontinuities Continuous function Conway base 13 function Image (mathematics) Derivative Extreme value theorem Fermat's theorem (stationary points) Intermediate value theorem Interval (mathematics) Theorem Topologist's sine curve Mean value theorem Real-valued function Real analysis Real number Theorems in real analysis
has abstract	In mathematics, Darboux's theorem is a theorem in real analysis, named after Jean Gaston Darboux. It states that every function that results from the differentiation of another function has the intermediate value property: the image of an interval is also an interval. When ƒ is continuously differentiable (ƒ in C1([a,b])), this is a consequence of the intermediate value theorem. But even when ƒ′ is not continuous, Darboux's theorem places a severe restriction on what it can be. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Darboux's_theorem_(analysis)
is Wikipage redirect of	Intermediate value property Intermediate value property of the derivative Darboux function Darboux continuity Darboux property Darboux theorem (analysis) Strongly Darboux function
is Link from a Wikipage to another Wikipage of	List of theorems Intermediate value property Intermediate value property of the derivative Antiderivative Differentiable function Jean Gaston Darboux Classification of discontinuities List of real analysis topics Conway base 13 function John Horton Conway Darboux function Fermat's theorem (stationary points) Intermediate value theorem Darboux continuity Darboux property Darboux theorem (analysis)
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Darboux's_theorem_(analysis)

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