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Optimization problems that involve finding the maxima or minima of functions also involve taking the first derivative of the function and finding locations where the value of the first derivative is equal to zero (by setting f'(x) = 0). The locations are either maxima, minima, or points of inflection and a second derivative test can be used to determine which of the three was found (max: f''(x) < 0, min: f''(x) > 0, PoI: f''(x) = 0).
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