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Darboux's theorem (analysis)

In real analysis, Darboux's theorem states that the derivative of any real-valued function of a real variable has the intermediate value property, that is, that the image of an interval is also an interval.

Darboux function, Further restrictions on derivatives & Proofs

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Overview

Statement of the theorem

Proofs

Darboux function

Further restrictions on derivatives

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Darboux's theorem (analysis)

Nodes30
Edges29
Triples0
Avg. degree1.93
Density0.066667
Components1

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displaystyle theorem function value darboux derivative real interval intermediate every f' point continuous darboux's varphi one set sets closed proof

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