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  "body": "\n## Definition\n\nLet $D \\subseteq \\mathbb{R}$, let $f \\colon D \\to \\mathbb{R}$, and let $a \\in D$.\nThe function $f$ has a local minimum at $a$ if there is $\\delta \u003e 0$ with $f(x) \\ge f(a)$ for all $x \\in D$ with $|x - a| \u003c \\delta$.\nIt is a strict local minimum if $f(x) \u003e f(a)$ for all such $x \\ne a$.\n\n## Remarks\n\nSo $f$ has a local minimum at $a$ exactly when $-f$ has a [[local maximum|00999TYPXB]] at $a$.\nFor example, $x^2$ has a strict local minimum at $0$.\nMathlib defines it as `IsLocalMin`.\n\n## Explanations\n\n### L1 human\n\nA local minimum is the bottom of a valley of the graph.\nNearby values are not lower.\n",
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