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  "body": "\n## Statement\n\nLet $I$ be an interval and let $f \\colon I \\to \\mathbb{R}$ be continuous, and differentiable at each interior point of $I$.\nIf $f'(x) \\ge 0$ for each interior point $x$ of $I$, then $f$ is increasing on $I$. That is, $f(x) \\le f(y)$ for $x \\le y$ in $I$.\n\n## Remarks\n\nThe proof uses the [[mean value theorem|0BARQY52N5]].\nFor differentiable $f$ on an open interval, the converse holds too: if $f$ is increasing, then $f' \\ge 0$.\nMathlib states it as `monotoneOn_of_deriv_nonneg`.\n\n## Explanations\n\n### L1 human\n\nIf the slope is never negative, the graph never goes down.\nIt may stay flat on some parts.\n",
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