"Rolle's theorem" meaning in All languages combined

{
  "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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  "lang_code": "en",
  "pos": "name",
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          "langcode": "en",
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      "glosses": [
        "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."
      ],
      "id": "en-Rolle's_theorem-en-name-bwrjUcHU",
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          "calculus",
          "calculus"
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          "real-valued"
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        [
          "differentiable",
          "differentiable"
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        [
          "function",
          "function"
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        [
          "point",
          "point"
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        [
          "derivative",
          "derivative"
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          "tangent"
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        [
          "graph",
          "graph"
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        [
          "zero",
          "zero"
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      "raw_glosses": [
        "(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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        "calculus",
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      "translations": [
        {
          "code": "it",
          "lang": "Italian",
          "sense": "theorem that a differentiable function with points of equal value must have a point of zero slope between them",
          "tags": [
            "masculine"
          ],
          "word": "teorema di Rolle"
        },
        {
          "code": "ru",
          "lang": "Russian",
          "roman": "teoréma Róllja",
          "sense": "theorem that a differentiable function with points of equal value must have a point of zero slope between them",
          "tags": [
            "feminine"
          ],
          "word": "теоре́ма Ро́лля"
        }
      ],
      "wikipedia": [
        "Michel Rolle",
        "Rolle's theorem"
      ]
    }
  ],
  "word": "Rolle's theorem"
}

{
  "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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      "glosses": [
        "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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          "graph",
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        ],
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          "zero",
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      "raw_glosses": [
        "(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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        "mathematics",
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      ],
      "wikipedia": [
        "Michel Rolle",
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      ]
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  "translations": [
    {
      "code": "it",
      "lang": "Italian",
      "sense": "theorem that a differentiable function with points of equal value must have a point of zero slope between them",
      "tags": [
        "masculine"
      ],
      "word": "teorema di Rolle"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "teoréma Róllja",
      "sense": "theorem that a differentiable function with points of equal value must have a point of zero slope between them",
      "tags": [
        "feminine"
      ],
      "word": "теоре́ма Ро́лля"
    }
  ],
  "word": "Rolle's theorem"
}