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  "body": "\n## Summary\n\nThe maximum of a real function on a set is its largest value, and the minimum is its smallest value.\nA point where the maximum or the minimum is attained is a global extremum; this is stronger than a [[local extremum|0WFBH1Q3WC]].\nA function need not attain a maximum, but by the [[extreme value theorem|0WS1A8E2P9]] a continuous function on a closed bounded interval does.\nFinding maxima and minima is the aim of optimization, and derivatives are the main tool.\n\n## Explanations\n\n### L1 human\n\nThe maximum of a function is the highest point of its graph, and the minimum is the lowest point.\nOn $[-1, 2]$, the function $x^2$ has its maximum $4$ at $x = 2$ and its minimum $0$ at $x = 0$.\nSome functions have no highest point: on the open interval $(0, 1)$, the function $x$ gets close to $1$ but never reaches it.\n",
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