1 / 22

Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH. IncreasingDecreasing. 1. f ’(x) > 0 for all x in I. f(x) increasing. 2. f(x) decreasing. f ’ (x) < 0 for all x in I. Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH. F091.

avani
Download Presentation

Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH Increasing\Decreasing 1 f ’(x) > 0 for all x in I f(x) increasing 2 f(x) decreasing f ’ (x) < 0 for all x in I

  2. Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH F091

  3. Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH F101

  4. Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH F102

  5. How do you know that: local maximum or local minimum First Derivative Test: 1 _ + 2 First Derivative Test: 1 _ + 2

  6. F081

  7. F083

  8. F102

  9. Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH Concavity 1 f ’’(x) > 0 for all x in I f(x) concave Up 2 f(x) concave Down f ’’(x) < 0 for all x in I

  10. Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH Example: Discuss the curve with respect to concavity, Concavity 1 f ’’(x) > 0 for all x in I f(x) concave Up 2 f(x) concave Down f ’’(x) < 0 for all x in I

  11. Concavity Test 1 f ’’(x) > 0 for all x in I f(x) concave Up

  12. Concavity Test 1 f ’’(x) < 0 for all x in I f(x) concave Down

  13. Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH F092

  14. Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH Inflection point: 1 _ + _ 2 +

  15. Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH Example: Find all inflection points of

  16. F091

  17. How do you know that: local maximum or local minimum second Derivative Test: 1 2 second Derivative Test: 1 2

  18. F081

  19. F091

  20. F091

  21. F083

More Related