Editing Rolle's theorem (section)

{{Short description|On stationary points between two equal values of a function}}
{{Calculus}}
[[File:RTCalc.svg|thumb|300 px|right|If a [[real number|real]]-valued function {{mvar|f}} is [[continuous function|continuous]] on a [[closed interval]] {{closed-closed|''a'', ''b''}}, [[derivative|differentiable]] on the [[open interval]] {{open-open|''a'', ''b''}}, and {{math|1=''f&thinsp;''(''a'') = ''f&thinsp;''(''b'')}}, then there exists a {{mvar|c}} in the open interval {{open-open|''a'', ''b''}} such that {{math|1=''f&thinsp;''′(''c'') = 0}}.]]

In [[calculus]], '''Rolle's theorem''' or '''Rolle's lemma''' essentially states that any real-valued [[differentiable function]] that attains equal values at two distinct points must have at least one point, somewhere between them, at which the slope of the tangent line is zero. Such a point is known as a [[stationary point]]. It is a point at which the first derivative of the function is zero. The theorem is named after [[Michel Rolle]].