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  "body": "\n## Summary\n\nThe central difference of a function $f$ with step $h$ is $\\delta_h f(x) = f(x + \\tfrac{h}{2}) - f(x - \\tfrac{h}{2})$.\nIt is symmetric around the point $x$.\nFor a smooth function, the quotient $\\delta_h f(x) / h$ approximates $f'(x)$ with an error of order $h^2$, better than the order $h$ of the one-sided quotients.\n\n## Explanations\n\n### L1 human\n\nTo estimate the slope of a curve at a point, you can look a little to the right and a little to the left of it, and compare.\nThe central difference does exactly this, with the point in the middle.\nFor $f(x) = x^2$ and step $h$ the result is $(x + h/2)^2 - (x - h/2)^2 = 2hx$.\nDividing by $h$ gives $2x$, which is the exact derivative, while a one-sided difference gives $2x + h$.\n",
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