See Rolle's theorem on Wiktionary
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"etymology_text": "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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"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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"(calculus) 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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"word": "теоре́ма Ро́лля"
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"word": "Teorema de Rolle"
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