{
  "aliases": null,
  "backlinks": [
    {
      "field": "specializes",
      "target": "07GR3TNW4H"
    },
    {
      "field": "specializes",
      "target": "0AEAHMFSCA"
    },
    {
      "field": "specializes",
      "target": "8FRWATNNMX"
    },
    {
      "field": "defines",
      "target": "0VV0HSW1ZS"
    },
    {
      "field": "uses",
      "target": "1JV7093B4C"
    },
    {
      "field": "uses",
      "target": "2JD72JT9FQ"
    },
    {
      "field": "uses",
      "target": "9NMMRYKBNG"
    },
    {
      "field": "uses",
      "target": "CVQVBMHH4X"
    },
    {
      "field": "uses",
      "target": "E820CTMJVM"
    },
    {
      "field": "uses",
      "target": "F0GBTYKN31"
    },
    {
      "field": "uses",
      "target": "GGEAGW4RRV"
    },
    {
      "field": "uses",
      "target": "M4RJHZ3KNA"
    },
    {
      "field": "uses",
      "target": "MQA1VVCJ63"
    },
    {
      "field": "uses",
      "target": "PDP7CHN4B4"
    },
    {
      "field": "uses",
      "target": "Q8MTV1Z4AQ"
    },
    {
      "field": "uses",
      "target": "TGWM8G5R0C"
    },
    {
      "field": "uses",
      "target": "TNMQDK0RR0"
    },
    {
      "field": "uses",
      "target": "V00Q05ZW1G"
    },
    {
      "field": "uses",
      "target": "V6XGZQ0GR1"
    },
    {
      "field": "uses",
      "target": "XZFYB2PBPD"
    },
    {
      "field": "uses",
      "target": "YBVSDT89T6"
    },
    {
      "field": "uses",
      "target": "ZGH5RYJTQC"
    },
    {
      "field": "about",
      "target": "3VB65PEZQS"
    },
    {
      "field": "about",
      "target": "FWKSHEJ9RP"
    }
  ],
  "body": "\n## Summary\n\nA convex function on an interval is a function whose graph lies on or below each of its chords. Convex functions have increasing slopes, and they satisfy Jensen's inequality. The node [[convex function|0VV0HSW1ZS]] gives the precise definition.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "26A51"
    ],
    "name": "Convex function",
    "same_as": {
      "wikidata": "Q319913",
      "wikipedia": "Convex function"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Convex_function"
      }
    ],
    "tag": "07Q7CNM5WF"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/07Q7CNM5WF/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/07Q7CNM5WF.md",
  "msc": [
    "26A51"
  ],
  "name": "Convex function",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/07Q/07Q7CNM5WF.md",
  "status": null,
  "tag": "07Q7CNM5WF",
  "uri": "m2://07Q7CNM5WF",
  "url": "https://tamnd.github.io/math2/wiki/convex-function/",
  "writing": {
    "tag": "07Q7CNM5WF",
    "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
      }
    ]
  }
}