"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.",
  "head_templates": [
    {
      "args": {},
      "expansion": "Rolle's theorem",
      "name": "en-proper noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English entries with language name categories using raw markup",
          "parents": [
            "Entries with language name categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Entries with translation boxes",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Italian translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Russian translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Calculus",
          "orig": "en:Calculus",
          "parents": [
            "Mathematical analysis",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "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",
      "links": [
        [
          "calculus",
          "calculus"
        ],
        [
          "theorem",
          "theorem"
        ],
        [
          "real-valued",
          "real-valued"
        ],
        [
          "differentiable",
          "differentiable"
        ],
        [
          "function",
          "function"
        ],
        [
          "point",
          "point"
        ],
        [
          "derivative",
          "derivative"
        ],
        [
          "tangent",
          "tangent"
        ],
        [
          "graph",
          "graph"
        ],
        [
          "zero",
          "zero"
        ]
      ],
      "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."
      ],
      "topics": [
        "calculus",
        "mathematics",
        "sciences"
      ],
      "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.",
  "head_templates": [
    {
      "args": {},
      "expansion": "Rolle's theorem",
      "name": "en-proper noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
      "categories": [
        "English entries with incorrect language header",
        "English entries with language name categories using raw markup",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English proper nouns",
        "English terms with non-redundant non-automated sortkeys",
        "English uncountable nouns",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Terms with Italian translations",
        "Terms with Russian translations",
        "en:Calculus"
      ],
      "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."
      ],
      "links": [
        [
          "calculus",
          "calculus"
        ],
        [
          "theorem",
          "theorem"
        ],
        [
          "real-valued",
          "real-valued"
        ],
        [
          "differentiable",
          "differentiable"
        ],
        [
          "function",
          "function"
        ],
        [
          "point",
          "point"
        ],
        [
          "derivative",
          "derivative"
        ],
        [
          "tangent",
          "tangent"
        ],
        [
          "graph",
          "graph"
        ],
        [
          "zero",
          "zero"
        ]
      ],
      "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."
      ],
      "topics": [
        "calculus",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Michel Rolle",
        "Rolle's theorem"
      ]
    }
  ],
  "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"
}