Speakur

Word Pronunciation & Dictionary

rolle's theorem

Word Rarity Very rare

Frequency: Zipf frequency 0.00 in modern English

Syllables
rolle's the-o-rem
IPA
18
Scrabble Score
13
Letters
3
Syllables
8
Unique Chars

Meaning

name

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.

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.

Questions

What does rolle's theorem mean?
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.
Where does rolle's theorem come from?
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.

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