1 / 21

The Mean Value Theorem

The Mean Value Theorem. Average Speed. = 78 mph. Average Speed. = 78 mph. Instantaneous Speed =. 78 mph . The Mean Value Theorem. Let f be continuous on [a, b] and differentiable on (a, b). Then there exists a point c in (a, b) such that:. a. c. b. The Mean Value Theorem.

talen
Download Presentation

The Mean Value Theorem

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. The Mean Value Theorem

  2. Average Speed = 78 mph

  3. Average Speed = 78 mph Instantaneous Speed = 78 mph

  4. The Mean Value Theorem Let f be continuous on [a, b] and differentiable on (a, b). Then there exists a point c in (a, b) such that: a c b

  5. The Mean Value Theorem Let f be continuous on [a, b] and differentiable on (a, b). Then there exists a point c in (a, b) such that: a c b

  6. The Mean Value Theorem Let f be continuous on [a, b] and differentiable on (a, b). Then there exists a point c in (a, b) such that: a c b

  7. Example Check that the hypothesis for the MVT is true for the function on the interval [0.5, 2].

  8. Example Check that the hypothesis for the MVT is true for the function on the interval [0.5, 2]. f(x) is not continuous at x = 0!

  9. Example Check that the hypothesis for the MVT is true for the function on the interval [0.5, 2]. f(x) is not continuous at x = 0! That’s okay because 0 is not in [0.5, 2]!

  10. Example Check that the hypothesis for the MVT is true for the function on the interval [0.5, 2]. f(x) is not continuous at x = 0! That’s okay because 0 is not in [0.5, 2]! f(x) is not differentiable at x = 0, again, that’s okay!

  11. Example If c is the value defined by the Mean Value Theorem, then for on [0, 1], what is the value of c?

  12. Example If c is the value defined by the Mean Value Theorem, then for on [0, 1], what is the value of c?

  13. Example If c is the value defined by the Mean Value Theorem, then for on [0, 1], what is the value of c?

  14. Example If c is the value defined by the Mean Value Theorem, then for on [0, 1], what is the value of c?

  15. Example If c is the value defined by the Mean Value Theorem, then for on [0, 1], what is the value of c? Now solve for x!

  16. Example If c is the value defined by the Mean Value Theorem, then for on [0, 1], what is the value of c? Now solve for x!

  17. Example If c is the value defined by the Mean Value Theorem, then for on [0, 1], what is the value of c? Now solve for x! Now find the roots using your calculator!

  18. Example If c is the value defined by the Mean Value Theorem, then for on [0, 1], what is the value of c? Now solve for x! Now find the roots using your calculator! This the c value of x that satisfies the MVT!

More Related