Скачать или смотреть Intervals of Increasing and Decreasing, Inflection Point from Graph

In this example problem, the graph of a polynomial function is given and we are tasked with identifying the intervals of increasing and decreasing as well as the point of inflection. To find the intervals of increasing and decreasing, we visualize walking on top of the graph while moving from left to right. When we are traveling uphill, we are increasing. When we are traveling downhill, we are decreasing. As we give the intervals for each it is important that we only use x-values. When our function exits the graph paper, we visualize it as continuing in the same direction forever and includes arrows, these will correspond with negative or positive infinity. When we have more than one interval on which the graph is increasing or decreasing, we include a union symbol U between the intervals. To identify the inflection point, we look at the concavity of the graph. When our graph changes from concave down (looking like the top of an umbrella) to concave up (looking like the bottom of a bowl), we get our inflection point.

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...