1st and 2nd Derivative Tests скачать в хорошем качестве

1st and 2nd Derivative Tests

In this example problem, we have a 3rd degree polynomial function and want to find maximum(s) and /or minimum(s). To do so, we take the first derivative and factor to find when it equals zero. These are our critical numbers (values) and the only place that we could have extrema. We then find the second derivative so that we can use the 2nd derivative test. We evaluate each critical number (value) into the 2nd derivative. If the result is positive, it tells us that our graph is concave up at that value and we will have a minimum. If the result is negative, our graph is concave down and we will have a maximum. We then confirm our results by using the 1st derivative test and placing our critical numbers (values) on a number line. We then test one value from each section of the number line into the first derivative to determine if that section of the number line is positive or negative. This informs us about when the original function is increasing or decreasing. If the function changes from increasing to decreasing, we have a maximum at that critical number (value). If the function changes from decreasing to increasing, we have a minimum at that critical number (value). 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...