Relative extrema refer to the highest or lowest points within a specific neighborhood of a function, while absolute extrema represent the highest or lowest points across the entire domain. Finding absolute extrema is more complex because it requires evaluating critical points, poles, and boundary behavior of the function. For example, a function may have multiple relative minima and maxima, but only one absolute minimum, especially if it approaches infinity at the boundaries. Understanding these differences is crucial for analyzing the behavior of functions in calculus. Overall, the distinction between relative and absolute extrema is fundamental in optimization problems.
