Create Presentation
Download Presentation

Download Presentation
## Second Derivative Test

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**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**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**Example**Determine areas of concavity for**Example**Determine where the graph is concave up and concave down**Inflection Points**Where a curve changes concavity**Example**Determine Inflection Points for**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**Example**Use the second derivative test to locate the extrema of