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Statements

Subject Item
dbr:Darboux's_theorem_(analysis)
rdfs:label
Darboux's theorem (analysis)
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.
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dbc:Theorems_in_calculus dbc:Continuous_mappings dbc:Articles_containing_proofs dbc:Theorems_in_real_analysis
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dbr:Theorem
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n11:Darboux's_theorem_(analysis)?oldid=1041456151&ns=0
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dbo: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.
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n11:Darboux's_theorem_(analysis)