Darboux’s theorem (analysis)
Let be a real-valued continuous function on , which is differentiable on , differentiable from the right at , and differentiable from the left at . Then the intermediate value theorem: for every between and , there is some such that .
Note that when is continuously differentiable (), this is trivially true by the intermediate value theorem. But even when is not continuous, Darboux’s theorem places a severe restriction on what it can be.
|Title||Darboux’s theorem (analysis)|
|Date of creation||2013-03-22 12:45:01|
|Last modified on||2013-03-22 12:45:01|
|Last modified by||mathwizard (128)|
|Synonym||intermediate value property of the derivative|