Intermediate Value Theorem
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(Redirected from Bolzano's intermediate value theorem)
The Intermediate Value Theorem is one of the very interesting properties of continous functions.
Statement
Proof
By Location of roots theorem,
such that
QED


![f:[a,b]\rightarrow\mathbb{R}](http://alt2.artofproblemsolving.com/Forum/latexrender/pictures/a/f/2/af24aa5c34caff3940ea28eff5926dae84c5bbd1.gif)

![[a,b]](http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/1/4/7/1475c39442659c6febe03b2e1809dbde6ec5fb5a.gif)


![g:[a,b]\rightarrow\mathbb{R}](http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/0/e/2/0e21263f4952829c8f7ed270f172c57a8d16a16c.gif)





