<?xml version="1.0" encoding="UTF-8"?>

<record version="9" id="422">
 <title>Rolle's theorem</title>
 <name>RollesTheorem</name>
 <created>2001-10-20 22:23:19</created>
 <modified>2005-03-06 13:27:09</modified>
 <type>Theorem</type>
 <creator id="3" name="drini"/>
 <author id="3" name="drini"/>
 <classification>
	<category scheme="msc" code="26A06"/>
 </classification>
 <related>
	<object name="IntermediateValueTheorem"/>
	<object name="MeanValueTheorem"/>
	<object name="ZeroesOfDerivativeOfComplexPolynomial"/>
 </related>
 <preamble>\usepackage[dvips]{graphicx}</preamble>
 <content>\textbf{Rolle's theorem.} If $f$ is a continuous function on $[a,b]$, such that $f(a)=f(b)$ and differentiable on $(a,b)$ then there exists a point $c\in(a,b)$ such that $f'(c)=0$.


\includegraphics{rolle}</content>
</record>
