Introduction to Analysis: Mean Value Theorem and Related Theorems

This resource delves into key concepts such as the Mean Value Theorem, Fermat's Theorem, Rolle's Theorem, Extreme Value Theorem, local maximums, and more. It presents important results and explores proofs in the context of analysis.

• Analysis
• Theorems
• Mean Value Theorem
• Fermats Theorem
• Extreme Values

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

2. Important Result y = (x ) f y = (x ) g f x g x = = If ( ) then ( ) ( ), ( ) g x + f x C ? ?

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 Local Maximum

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

8. The Extreme Value Theorem The Extreme Value Theorem

9. Fermats Theorem Fermat s Theorem

10. Lemma (HW)

11. Fermats Theorem Fermat s Theorem

12. Conceptual Diagrams

13. Fermats Theorem Fermat s Theorem

14. Fermats Theorem Fermat s Theorem

15. Fermats Theorem Fermat s Theorem

16. Fermats Theorem Fermat s Theorem

17. Proof Proof

18. Proof Proof

19. Proof Proof

20. Proof Proof

21. Rolles Theorem Rolle s Theorem

22. Rolles Theorem Rolle s Theorem

23. Rolles Theorem Rolle s Theorem

24. Rolles Theorem Rolle s Theorem

25. Rolles Theorem Rolle s Theorem

26. Rolles Theorem Rolle s Theorem

27. Rolles Theorem Rolle s Theorem

28. Rolles Theorem Rolle s Theorem

29. Rolles Theorem Rolle s Theorem

30. Rolles Theorem Rolle s Theorem

31. Rolles Theorem Rolle s Theorem

32. Rolles Theorem Rolle s Theorem

33. Rolles Theorem Rolle s Theorem

34. Rolles Theorem Rolle s Theorem

35. Rolles Theorem Rolle s Theorem

36. Rolles Theorem Rolle s Theorem

37. Rolles Theorem Rolle s Theorem

38. Rolles Theorem Rolle s Theorem

39. Rolles Theorem Rolle s Theorem

40. Rolles Theorem Rolle s Theorem

41. Proof Proof

42. Proof Proof

43. The Mean Value Theorem The Mean Value Theorem

44. The Mean Value Theorem The Mean Value Theorem

45. The Mean Value Theorem The Mean Value Theorem

46. The Mean Value Theorem The Mean Value Theorem

47. The Mean Value Theorem The Mean Value Theorem

48. The Mean Value Theorem The Mean Value Theorem

49. The Mean Value Theorem The Mean Value Theorem

50. The Mean Value Theorem The Mean Value Theorem

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