Rolle's theorem

proper noun

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.

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Meanings

proper noun
  1. calculusThe 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.

Origin

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.

Full word history & related roots →

Translations

Bulgarian теорема на Рол
  • теорема на Рол (teorema na Rol)theorem that a differentiable function with points of equal value must have a point of zero slope between them
French théorème de Rolle
  • théorème de Rolletheorem that a differentiable function with points of equal value must have a point of zero slope between them
Italian teorema di Rolle
  • teorema di Rolletheorem that a differentiable function with points of equal value must have a point of zero slope between them
Polish twierdzenie Rolle'a
  • twierdzenie Rolle'atheorem that a differentiable function with points of equal value must have a point of zero slope between them
Portuguese Teorema de Rolle
  • Teorema de Rolletheorem that a differentiable function with points of equal value must have a point of zero slope between them
Russian теоре́ма Ро́лля
  • теоре́ма Ро́лля (teoréma Róllja)theorem that a differentiable function with points of equal value must have a point of zero slope between them
Spanish teorema de Rolle
  • teorema de Rolletheorem that a differentiable function with points of equal value must have a point of zero slope between them
Cite this entry
APA

Rolle's theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Rolle's%20theorem

MLA

“Rolle's theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Rolle's%20theorem. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Rolle's theorem,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Rolle's%20theorem.

Source: Rolle's theorem on Wiktionary, CC BY-SA 4.0.