Rolle's theorem en · PROPN
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.
Meanings
- 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 is differentiable on (a,b) and f(a)=f(b) then ∃c∈(a,b):f'(c)=0.
Translations (7)
fr théorème de Rolle (theorem that a differentiable function with points of equal value must have a point of zero slope between them) · pl twierdzenie Rolle'a (theorem that a differentiable function with points of equal value must have a point of zero slope between them) · bg теорема на Рол (theorem that a differentiable function with points of equal value must have a point of zero slope between them) · es teorema de Rolle (theorem that a differentiable function with points of equal value must have a point of zero slope between them) · it teorema di Rolle (theorem that a differentiable function with points of equal value must have a point of zero slope between them) · pt Teorema de Rolle (theorem that a differentiable function with points of equal value must have a point of zero slope between them) · ru теоре́ма Ро́лля (theorem that a differentiable function with points of equal value must have a point of zero slope between them)