Rolle's theorem

== English == === Etymology === Named after French mathematician Michel Rolle (1652–1719), although his 1691 proof covered only the case of polynomial functions and did not use the methods of differential calculus. === Proper noun === Rolle's theorem (calculus) The theorem that any real-valued differentiable function that attains equal values at two distinct points must have a point somewhere between them where the first derivative (the slope of the tangent line to the graph of the function) is zero. In mathematical terms, if f : R → R {\displaystyle f:\mathbb {R} \rightarrow \mathbb {R} } is differentiable on ( a , b ) {\displaystyle (a,b)} and f ( a ) = f ( b ) {\displaystyle f(a)=f(b)} then ∃ c ∈ ( a , b ) : f ′ ( c ) = 0 {\displaystyle \exists c\in (a,b):f'(c)=0} . ==== Translations ====