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  "body": "\n## Definition\n\nLet $I$ be an open interval, let $f \\colon I \\to \\mathbb{R}$, and let $a \\in I$.\nThe point $a$ is a critical point of $f$ if either $f$ is not differentiable at $a$, or $f$ is differentiable at $a$ with $f'(a) = 0$.\nIn the second case, $a$ is also called a stationary point.\n\n## Remarks\n\nBy [[Fermat's theorem|0PCVBRV9VJ]], each local extremum of $f$ in $I$ is a critical point.\nThe converse fails: $x^3$ has a critical point at $0$, but no local extremum.\nFor $|x|$, the point $0$ is a critical point where $f$ is not differentiable.\n\n## Explanations\n\n### L1 human\n\nCritical points are the candidates for local maxima and minima.\nThere the tangent is horizontal, or there is no tangent at all.\n",
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