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  "body": "\n## Definition\n\nLet $I$ be an interval and let $f \\colon I \\to \\mathbb{R}$ be a function.\nThe function $f$ is concave if\n$$f(t x + (1 - t) y) \\ge t f(x) + (1 - t) f(y)$$\nfor all $x, y \\in I$ and all $t \\in [0, 1]$.\n\n## Remarks\n\nSo $f$ is concave exactly when $-f$ is [[convex|0VV0HSW1ZS]].\nFor example, $\\sqrt{x}$ and $\\ln x$ are concave on $(0, \\infty)$.\nMathlib defines concavity on a set as `ConcaveOn`.\n\n## Explanations\n\n### L1 human\n\nA concave function bends downward, like a dome.\nEach chord of the graph lies on or below the graph.\n",
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