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## Section 4.4

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**Section 4.4**Concavity and the Second Derivative Test**Example 1**State the signs of and on the interval (0,2).**Example 2**State the signs of and on the interval (0,2).**Example 3**Determine the open intervals on which the graph is concave upward or concave downward.**Example 4**Determine the open intervals on which the graph is concave upward or concave downward.**Example 5**Determine the open intervals on which the graph is concave upward or concave downward.**Inflection Points**• Examples:**How do we find them?**• So . . . • Take the second derivative. • Find out where it is zero or undefined. • These are your possible inflection points. • Only an inflection point if the concavity changes.**Example 6**Find the points of inflection and discuss the concavity of the graph of the function.**Example 7**Find the points of inflection and discuss the concavity of the graph of the function.**Example 8**Find the points of inflection and discuss the concavity of the graph of the function.**Example 9**Find all relative extrema. Use the Second Derivative Test where applicable.**Example 10**Find all relative extrema. Use the Second Derivative Test where applicable.**Example 11**Find all relative extrema. Use the Second Derivative Test where applicable.**Questions?**Be sure to be practicing the given problem sets!