{
  "aliases": [
    "minimax-point"
  ],
  "backlinks": [
    {
      "field": "defines",
      "target": "00N3T18QNA"
    }
  ],
  "body": "\n## Summary\n\nA saddle point of a differentiable function of several variables is a critical point that is not a [[local extremum|0WFBH1Q3WC]].\nNear a saddle point, the function takes values both larger and smaller than its value at the point.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "aliases": [
      "minimax-point"
    ],
    "kind": "concept",
    "msc": [
      "26B05"
    ],
    "name": "Saddle point",
    "same_as": {
      "wikidata": "Q690935",
      "wikipedia": "Saddle point"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Saddle_point"
      }
    ],
    "tag": "0JW6MDHAZD",
    "uses": [
      "0WFBH1Q3WC",
      "0ABK9V9Y64"
    ]
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/0JW6MDHAZD/",
  "links": [
    {
      "field": "uses",
      "target": "0WFBH1Q3WC"
    },
    {
      "field": "uses",
      "target": "0ABK9V9Y64"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/0JW6MDHAZD.md",
  "msc": [
    "26B05"
  ],
  "name": "Saddle point",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0JW/0JW6MDHAZD.md",
  "status": null,
  "tag": "0JW6MDHAZD",
  "uri": "m2://0JW6MDHAZD",
  "url": "https://math2.tamnd.com/wiki/saddle-point/",
  "writing": {
    "tag": "0JW6MDHAZD",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}
