Absolute Extrema. If a function has an absolute maximum at x = b , then f (b) is the largest value that f can attain. Similarly, if a function has an absolute minimum at x = b , then f (b) is the smallest value that f can attain.
The strategy for tracking the sign of the derivative is useful for more than determining where a function is increasing or decreasing. It is also useful for locating the relative extrema of a function. At a relative extrema, a function changes from increasing to decreasing or decreasing to increasing.
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