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  "body": "\n## Definition\n\nLet $I$ be an open interval and let $f \\colon I \\to \\mathbb{R}$ be differentiable on $I$.\nIf $f'$ is differentiable at $a \\in I$, the second derivative of $f$ at $a$ is $f''(a) = (f')'(a)$.\n\n## Remarks\n\nIt is the [[higher derivative|084NGSTWM7]] $f^{(2)}$. Another notation is $\\frac{d^2 f}{dx^2}$.\nIf $f'' \u003e 0$ on $I$, then $f$ is [[convex|0VV0HSW1ZS]] on $I$.\nIn mechanics, if $f(t)$ is the position at time $t$, then $f''(t)$ is the acceleration.\n\n## Explanations\n\n### L1 human\n\nThe second derivative is the rate of change of the slope.\nIt tells how the graph bends: upward where $f'' \u003e 0$ and downward where $f'' \u003c 0$.\n",
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