A local extremum is a point on a curve or surface that is either a local maximum or a local minimum. In other words, it is a point where the value of the function is either higher or lower than all nearby points, but not necessarily the highest or lowest point on the entire curve or surface.

Local extrema can be found by analytically by using either the first derivative test or the second derivative test. Alternatively local extrema can be found graphically by looking where the graph reaches a peak, hill, valley, or dip.

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