Rolle's theorem

Etymology
Named after French mathematician (1652–1719), although his 1691 proof covered only the case of polynomial functions and did not use the methods of differential calculus.

Proper noun

 * 1)  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 $$f : \mathbb{R} \rightarrow \mathbb{R}$$ is differentiable on $$(a,b)$$ and $$f(a)=f(b)$$ then $$\exists c \in (a,b) : f'(c)=0$$.

Translations

 * Italian: teorema di Rolle
 * Russian: теоре́ма Ро́лля