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  "body": "\n## Statement\n\nLet $f$ be a real function on an open interval $(c - \\delta, c + \\delta)$ with $\\delta \u003e 0$, continuous at $c$ and differentiable at each $x \\ne c$.\nIf $f'(x) \\le 0$ for $c - \\delta \u003c x \u003c c$ and $f'(x) \\ge 0$ for $c \u003c x \u003c c + \\delta$, then $f$ has a [[local minimum|0NS8BP96QX]] at $c$.\nIf the inequalities are reversed, then $f$ has a local maximum at $c$.\n\n## Remarks\n\nThe function is [[decreasing on the left and increasing on the right|026BJBQNGJ]] of $c$.\nThe test needs no derivative at $c$. It works for $|x|$ at $0$.\nMathlib states the minimum case as `isLocalMin_of_deriv`.\n\n## Explanations\n\n### L1 human\n\nIf the graph goes down until $c$ and then goes up, the point $c$ is the bottom of a valley.\n",
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