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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 maximum at $a$ if there is $\\delta \u003e 0$ with $f(x) \\le f(a)$ for all $x \\in D$ with $|x - a| \u003c \\delta$.\nIt is a strict local maximum if $f(x) \u003c f(a)$ for all such $x \\ne a$.\n\n## Remarks\n\nA global maximum, where $f(x) \\le f(a)$ for all $x \\in D$, is also a local maximum.\nA [[local minimum|0NS8BP96QX]] is defined with $f(x) \\ge f(a)$. Local maxima and minima are local extrema.\nAt an interior local extremum, a differentiable function has [[derivative zero|0PCVBRV9VJ]].\nMathlib defines it as `IsLocalMax`.\n\n## Explanations\n\n### L1 human\n\nA local maximum is a hilltop of the graph.\nNearby values are not higher, although values far away may be higher.\n",
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