1. 3.4 Concavity and the Second Derivative Test

2. Example 1: The stocks of two companies, A and B,
went up in value, and both currently sell for $75. However, one I clearly a better investment than the other. Explain in terms of concavity.

3. Test for Inflection Points: Assume that f ” (x) exists.
If f ” (c) = 0 and f ” (x) changes sign at x = c, then
f(x) has a point of inflection at x = c.
Point of inflection: (c, f(c))

4. Example 2: Find the points of inflection of
and intervals of concavity of

5. Example 4: Find the points of inflection of
Second Derivative Test for Critical Points

7. Example 5: Analyze the critical points of

9. Graph Sketching and Asymptotes
In the following examples, find all the critical points
(transition points), intervals of increase/decrease,
concavity, and asymptotic behavior, if exists. Then
Sketch the graph, with this information indicated.