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Day 1 meaning of derivative.notebook 1 August 21, 2016

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Page 1: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

1

August 21, 2016

Page 2: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

2

August 21, 2016

Page 3: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

3

August 21, 2016

Page 4: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

4

August 21, 2016

Page 5: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

5

August 21, 2016

Page 6: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

6

August 21, 2016

Page 7: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

7

August 21, 2016

Page 8: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

8

August 21, 2016

Page 9: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

9

August 21, 2016

Page 10: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

10

August 21, 2016

Page 11: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

11

August 21, 2016

Page 12: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

12

August 21, 2016

f ' (x) = ­2x

Page 13: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

13

August 21, 2016

When to use this version:

You are given a specific x value to evaluate the derivative at.i.e. find the derivative at 3:  notation f' (3)

Page 14: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

14

August 21, 2016

Page 15: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

15

August 21, 2016

Page 16: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

16

August 21, 2016

Page 17: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

17

August 21, 2016

Page 18: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

18

August 21, 2016

Page 19: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

19

August 21, 2016

using the formal definition and then the alternative defn.Then find the equation of the

tangent line and normal line

at x = 3.

Page 20: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

20

August 21, 2016

using the formal definition and then the alternative defn.Then find the equation of the

tangent line and normal line

at x = 3.

Page 21: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

21

August 21, 2016

Page 22: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

22

August 21, 2016

Page 23: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

23

August 21, 2016

Page 24: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

24

August 21, 2016

Page 25: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

25

August 21, 2016

Page 26: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

26

August 21, 2016

Page 27: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

27

August 21, 2016

Page 28: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

28

August 21, 2016

Page 29: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

29

August 21, 2016

Do # 3, 4, 14, 15 abc

Page 30: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

30

August 21, 2016

Page 31: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

31

August 21, 2016

Page 32: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

32

August 21, 2016

Page 33: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

33

August 21, 2016

Page 34: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

34

August 21, 2016

Page 35: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

35

August 21, 2016

Then find the equation of the

tangent line and normal line

at x = ­2.

Page 36: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

36

August 21, 2016

Page 37: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

37

August 21, 2016

Page 38: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

38

August 21, 2016

Page 39: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

39

August 21, 2016

Page 40: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

40

August 21, 2016

Page 41: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

41

August 21, 2016

Derivatives from a Chart!  College Bd requirement

Page 42: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

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August 21, 2016

When is a graph differentiableA graph is not differentiable anywhere the following is true:

cusp

corner

discontinuity:  removable

    infinite

jump

vertical tangent

Page 43: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

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August 21, 2016

Page 44: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

44

August 21, 2016

Page 45: Day 1 meaning of derivative.notebook€¦ · Day 1 meaning of derivative.notebook 19 August 21, 2016 using the formal definition and then the alternative defn. Then find the equation

Day 1 meaning of derivative.notebook

45

August 21, 2016