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Second Derivative Test

Second Derivative Test. Concavity. If the graph of a function f lies above all of its tangents, then it is called concave upward If the graph of a function f lies below all of its tangents, then it is called concave downward. Test for Concavity.

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Second Derivative Test

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  1. Second Derivative Test

  2. Concavity If the graph of a function flies above all of its tangents, then it is called concave upward If the graph of a function flies below all of its tangents, then it is called concave downward

  3. Test for Concavity If f’’ > 0 for all x in an interval, then the graph is concave upward If f’’ < 0 for all x in an interval, then the graph is concave downward

  4. Example Determine areas of concavity for

  5. Example Determine where the graph is concave up and concave down

  6. Inflection Points Where a curve changes concavity

  7. Example Determine Inflection Points for

  8. Second Derivative Test The second derivative can be used to identify local max and min values as well If f’ = 0 and the second derivative exists on an interval 1) If f’’(c)> 0, then this c is a minimum 2) If f’’(c) < 0, then this c is a maximum

  9. Example Use the second derivative test to locate the extrema of

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