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MAT 3749 Introduction to Analysis

MAT 3749 Introduction to Analysis. Section 2.3 Part III The Mean Value Theorem. http://myhome.spu.edu/lauw. Important Result. a. b. Preview. Extreme Value Theorem Fermat’s Theorem Rolle’s Theorem The Mean Value Theorem. References. Section 2.3. Maximum Value. Local Maximum. T or F.

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MAT 3749 Introduction to Analysis

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  1. MAT 3749Introduction to Analysis Section 2.3 Part III The Mean Value Theorem http://myhome.spu.edu/lauw

  2. Important Result a b

  3. Preview • Extreme Value Theorem • Fermat’s Theorem • Rolle’s Theorem • The Mean Value Theorem

  4. References • Section 2.3

  5. Maximum Value

  6. Local Maximum

  7. T or F An absolute max is a local max.

  8. The Extreme Value Theorem

  9. Fermat’s Theorem

  10. Lemma (HW)

  11. Fermat’s Theorem

  12. Conceptual Diagrams

  13. Fermat’s Theorem

  14. Fermat’s Theorem

  15. Fermat’s Theorem

  16. Fermat’s Theorem

  17. Proof

  18. Proof

  19. Proof

  20. Proof

  21. Rolle’s Theorem

  22. Rolle’s Theorem

  23. Rolle’s Theorem

  24. Rolle’s Theorem

  25. Rolle’s Theorem

  26. Rolle’s Theorem

  27. Rolle’s Theorem

  28. Rolle’s Theorem

  29. Rolle’s Theorem

  30. Rolle’s Theorem

  31. Rolle’s Theorem

  32. Rolle’s Theorem

  33. Rolle’s Theorem

  34. Rolle’s Theorem

  35. Rolle’s Theorem

  36. Rolle’s Theorem

  37. Rolle’s Theorem

  38. Rolle’s Theorem

  39. Rolle’s Theorem

  40. Rolle’s Theorem

  41. Proof

  42. Proof

  43. The Mean Value Theorem

  44. Proof

  45. The Mean Value Theorem

  46. The Mean Value Theorem

  47. The Mean Value Theorem

  48. Theorem (Consequence) If f’(x)=0 for all x in an interval (a,b), then f is constant on (a,b). Q: Can we apply the MVT directly?

  49. Corollary (Important) a b

  50. Corollary (Important) a b

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