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for questions involving inequalities, upper and lower bounds.

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Non-negativity of a complicated function

If you can bound $f'(x)$, you only need to numerically evaluate finitely many points to show that the function is positive everywhere. (Given $-A < f'(x) < A$, if $f(x_0) = C$, take $x_1 = x_0 + C/A$. …
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