Download
second derivative test n.
Skip this Video
Loading SlideShow in 5 Seconds..
Second Derivative Test PowerPoint Presentation
Download Presentation
Second Derivative Test

Second Derivative Test

112 Views Download Presentation
Download Presentation

Second Derivative Test

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

  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