Editing Rolle's theorem (section)

== Standard version of the theorem ==

If  a [[real number|real]]-valued [[Function (mathematics)|function]] {{mvar|f}} is [[continuous function|continuous]] on a proper [[closed interval]] {{closed-closed|''a'',&nbsp;''b''}}, [[Differentiable function|differentiable]] on the [[open interval]] {{open-open|''a'', ''b''}}, and {{math|1=''f&thinsp;''(''a'') = ''f&thinsp;''(''b'')}}, then there exists at least one {{mvar|c}} in the open interval {{open-open|''a'', ''b''}} such that <math display="block">f'(c) = 0.</math>

This version of Rolle's theorem is used to prove the [[mean value theorem]], of which Rolle's theorem is indeed a special case. It is also the basis for the proof of [[Taylor's theorem]].