Concavity and the Second Derivative Test
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Lesson Summary:
In this lesson, we learn about concavity and the second derivative test for local extrema. We see that a graph is concave up if the slope is increasing, and concave down if the slope is decreasing. We also learn how to use the second derivative to determine the concavity of the graph, and apply the second derivative test to classify critical numbers as local maximum or minimum values.
Lesson Description:
Concavity and the second derivative. The second derivative test for local extrema.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
Additional Resources:
- Concavity and Points of Inflection - Practice with Concavity and Points of Inflection.
Questions answered by this video:
- What is concavity?
- What is the second derivative test?
- How can you tell when a graph is concave up or concave down?
- What does it mean for a graph to be concave up or concave down?
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Staff Review
This video explains the ins and outs of graphs being concave up or concave down. Several examples and pictures are used to hit home the point. The second derivative test is used to find inflection points and determine where a graph is concave up or concave down. Critical points and local extrema are revisited. There is not a lot of new terminology in this video, and there are many different useful example problems.
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