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Rolle's theorem

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.

Proper noun

Rolle's theorem

  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:ℝ→ℝ is differentiable on (a,b) and f(a)=f(b) then ∃c∈(a,b):f'(c)=0.

Origin of Rolle's theorem

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.

Questions about Rolle's theorem

What does Rolle's theorem mean?
Rolle's theorem means 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.
What part of speech is Rolle's theorem?
Rolle's theorem is a proper noun.

Words near Rolle's theorem in the dictionary

  1. rollcalling
  2. rollcalls
  3. rolldown
  4. rolldowns
  5. Rolle
  6. Rolle's theorem
  7. rolled
  8. rolled about
  9. rolled around
  10. rolled away
  11. rolled back

Source and license

Adapted from Wiktionary: Rolle's theorem (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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