A local maximum refers to the highest point of a function within a specific interval. It is higher than all nearby points but may not be higher than all other points on the entire function.
Imagine you're at a concert, and you're standing on top of a hill in the crowd. The local maximum would be like being at the tallest point around, even though there might be taller people elsewhere in the venue.
Absolute Maximum: An absolute maximum refers to the highest point of an entire function across its entire domain.
Decreasing Interval: A decreasing interval is an interval on which every y-value (output) of a function is less than any previous y-value within that interval.
Second Derivative Test: The second derivative test helps determine whether critical points are relative maxima or minima by analyzing concavity based on derivatives.
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