1. Derivative of a Function Chapter 3.1

2. Definition of the Derivative 2

3. 3

4. 4

5. Example 1: Applying the Definition 5

6. 6

7. 7

8. 8

9. Alternate Definition 9

10. Example 2: Applying the Alternate Definition 10

11. Example 2: Applying the Alternate Definition 11

12. Example 2: Applying the Alternate Definition 12

13. Notation 13

14. 14

15. 15

16. 16

17. 17

18. 18

19. 19

20. Example 5: Downhill Skier (Prob. 29) 20

21. Example 5: Downhill Skier (Prob. 29) Time (seconds)Distance (feet) 00 13.3 213.3 329.9 453.2 583.2 6119.8 7163.0 8212.9 9269.5 10332.7 21

22. Example 5: Downhill Skier (Prob. 29) 22

23. Example 5: Downhill Skier (Prob. 29) 23

24. Example 5: Downhill Skier (Prob. 29) 24

25. One-Sided Derivatives 25

26. One-Sided Derivatives 26

27. Example 6: One-Sided Derivatives Can Differ at a Point 27

28. Example 6: One-Sided Derivatives Can Differ at a Point 28

29. Example 6: One-Sided Derivatives Can Differ at a Point 29

30. Exercise 3.1 30