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  "body": "\n## Statement\n\nLet $I$ be an open interval, let $f \\colon I \\to \\mathbb{R}$, and let $a \\in I$.\nIf $f$ is [[differentiable|0A61B60B5R]] at $a$, then $f$ is [[continuous at|0EEE2CZB2A]] $a$.\n\n## Remarks\n\nFor $x \\ne a$, write $f(x) - f(a) = \\frac{f(x) - f(a)}{x - a} \\cdot (x - a)$. The first factor tends to $f'(a)$ and the second to $0$.\nThe converse fails. The [[absolute value|0CQ9ZM383N]] is continuous but not differentiable at $0$. The [[Weierstrass function|01A0MK1730]] is continuous and nowhere differentiable.\nMathlib states it as `HasDerivAt.continuousAt`.\n\n## Explanations\n\n### L1 human\n\nIf a graph has a tangent line at a point, it cannot jump there.\nA jump would make the slopes of the secant lines blow up.\n",
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