Rolle's theorem

English

Etymology

Named after French mathematician Template:W (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. Template:Lb 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 $f:ℝ\to ℝ$ is differentiable on $(a,b)$ and $f(a)=f(b)$ then $\mathrm{\exists }c\in (a,b):f^{\prime }(c)=0$.

Translations

• Italian: Template:T
• Russian: Template:T