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1 When you see… Find the zeros You think…. 2 To find the zeros...

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Presentation on theme: "1 When you see… Find the zeros You think…. 2 To find the zeros..."— Presentation transcript:

1 1 When you see… Find the zeros You think…

2 2 To find the zeros...

3 3 When you see… Find equation of the line tangent to f(x) at (a, b) You think…

4 4 Equation of the tangent line

5 5 You think… When you see… Find equation of the line normal to f(x) at (a, b)

6 6 Equation of the normal line

7 7 You think… When you see… Find the interval where f(x) is increasing

8 8

9 9 You think… When you see… Find the interval where f’ (x) is increasing

10 10 Slope of f (x) is increasing

11 11 You think… When you see… Find critical numbers

12 12 Find critical numbers

13 13 You think… When you see… Find inflection points

14 14 Find inflection points

15 15 You think… When you see… Show that exists

16 16

17 17 You think… When you see… Show that f(x) is continuous

18 18. f(x) is continuous

19 19 You think… When you see… Show that f(x) is differentiable at x = a

20 20 f(x) is differentiable

21 21 You think… When you see… Find vertical asymptotes of f(x)

22 22 Find vertical asymptotes of f(x) VA: Set denominator = 0 Note: it’s a hole (not a VA) if top = 0

23 23 You think… When you see… Find horizontal asymptotes of f(x)

24 24 Find horizontal asymptotes of f(x)

25 25 You think… When you see… Find the average rate of change of f(x) at [a, b]

26 26 Average rate of change of f(x) Find ARC(f) = f (b) - f ( a) b - a

27 27 You think… When you see… Find the instantaneous rate of change of f(x) at x = a

28 28 Instantaneous rate of change of f(x) Find f ‘ ( a)

29 29 You think… When you see… Find the(absolute) max or minimum value of a function

30 30 Local Minimum value of a function

31 31 You think… When you see… Show that the only CP is a max/min

32 32 Local Minimum value of a function

33 33 You think… When you see… Given s(t) (position function), find v(t)

34 34 Given position s(t), find v(t)

35 35 You think… When you see… Total Distance

36 36 Given v(t), find how far a particle travels on [a,b]

37 37 You think… When you see… Find the average velocity of a particle on [ a, b ]

38 38 Find the average rate of change on [a,b]

39 39 You think… When you see… determine if a particle is speeding up

40 40 Given v(t), determine if the particle is speeding up

41 41 You think… When you see… Mean Value Theorem

42 42 Show that the MVT holds on [a,b]

43 43 You think… When you see… Relationship between f f’ and f’’

44 44 f” + - f’ + - f

45 45 You think… When you see… Find f ’(x) by definition

46 46 Find f ‘( x) by definition

47 47 You think… When you see… FTC part 2.

48 48 FTC

49 49 You think… When you see…

50 50 FTC part 2

51 51 You think… When you see…

52 52 Fundamental Theorem, again

53 53 You think… When you see… Find the derivative of the inverse of f(x) at x = a

54 54 Derivative of the inverse of f(x)

55 55 You think… When you see… y is increasing proportionally to y

56 56

57 57 You think… When you see… The rate of change of population is …

58 58 Rate of change of a population

59 59 You think… When you see… Find area using Riemann/Trapezoidal sums

60 60 Area using Riemann sums

61 61 You think… When you see… Solve the differential equation …

62 62 Solve the differential equation...

63 63 You think… When you see… Given a base, cross sections perpendicular to the x-axis that are

64 64

65 65 You think… When you see… Find where the tangent line to f(x) is horizontal

66 66

67 67 You think… When you see… Find where the tangent line to f(x) is vertical

68 68

69 69 You think… When you see… Find the derivative of f(g(x))

70 70 Find the derivative of f(g(x)) Think... Chain Rule

71 71 You think… When you see… estimate where c is between a and b.

72 72 MVT

73 73 You think… When you see… Approximate f(c) using linearization

74 74

75 75 You think… When you see… Volume of Revolution

76 76 (1) dx or dy, (2) washer or disk, …

77 77 You think… When you see… Find the area between curves f(x) and g(x)

78 78 Area between f(x) and g(x) on [a,b]

79 79 You think… When you see…

80 80 Average value of the function

81 81 You think… When you see…

82 82

83 83 You think… When you see…

84 84

85 85 You think… When you see…

86 f ’(x) 86

87 87 You think… When you see…

88 U substitution 88


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