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All local maximums and minimums on a function’s graph — called local extrema — occur at critical points of the function (where the derivative is zero or undefined). Don’t forget, though, that not all critical points are necessarily local extrema. Can absolute extrema be local extrema? A local extremum (orRead More →

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When f is defined on a closed interval, there is no open interval containing an endpoint of the closed interval on which f is defined. Hence, a local extreme value cannot occur at the endpoint of an interval of domain. Are endpoints relative extrema? Relative extrema can certainly occur atRead More →