Global Maximum and Minimum
In this example calculus problem, we are given a 3rd degree polynomial and an interval and asked to find the global (absolute) maximum (max) and global (absolute) minimum (min). To do so, we find the first derivative and factor it. We then determine the values of x that will make it equal to zero. These are referred to as critical values (numbers) and are the only values that our function could have local (relative) maximums or minimums. We then evaluate our original function at each of these critical values (numbers) AND at the endpoints of our given interval. We then compare the outputs and the largest is the global (absolute) maximum on that interval while the smallest is the global (absolute) minimum on that interval.
This video contains examples that are from Business Calculus, 1st ed, by Calaway, Hoffman, Lippman. from the Open Course Library, remixed from Dale Hoffman's Contemporary Calculus text. It was extended by David Lippman to add several additional topics. The text is licensed under the Creative Commons Attribution license. http://creativecommons.org/licenses/b...
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