Key formulas include $f'(x) > 0$ for increasing, $f'(x) < 0$ for decreasing, $f'(x) = 0$ and $f''(x) > 0$ for minima, $f'(x) = 0$ and $f''(x) < 0$ for maxima, and $f''(x) = 0$ for points of inflection.
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