3.4 Concavity and the Second Derivative Test

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Presentation transcript:

3.4 Concavity and the Second Derivative Test

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.

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))

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

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

Example 5: Analyze the critical points of

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.