1 When you see… Find the zeros You think…

2 To find the zeros...

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

4 Equation of the tangent line

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

6 Equation of the normal line

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

8 f(x) increasing

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

10 Slope of f (x) is increasing

11 You think… When you see… Find the minimum value of a function

12 Local Minimum value of a function

13 You think… When you see… Find critical numbers

14 Find critical numbers

15 You think… When you see… Find inflection points

16 Find inflection points

17 You think… When you see… Show that exists

18 Show exists Show that

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

20. f(x) is continuous

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

22 f(x) is differentiable

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

24 Find holes/vertical asymptotes of f(x) Factor/cancel f(x) VA: Set denominator = 0 Hole: where factor that cancels = 0

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

26 Find horizontal asymptotes of f(x)

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

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

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

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

31 You think… When you see…

32 Average value of the function

33 You think… When you see… Find the absolute maximum of f(x) on [a, b]

34 Find the absolute maximum/Min of f(x)

35 You think… When you see… Show that a piecewise function is differentiable at the point a where the function rule splits

36 Show a piecewise function is differentiable at x=a

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

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

39 You think… When you see… Total Distance

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

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

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

43 You think… When you see… Given v(t), determine if a particle is speeding up at t = k

44 Given v(t), determine if the particle is speeding up at t=k

45 You think… When you see… Given v(t) and s(0), find s(t)

46 Given v(t) and s(0), find s(t)

47 You think… When you see… Mean Value Theorem

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

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

50 Find f ‘( x) by definition

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

52 Derivative of the inverse of f(x)

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

54 y is increasing proportionally to y. y is increasing proportionally to y

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

56 Rate of change of a population

57 You think… When you see…

58 Fundamental Theorem

59 You think… When you see…

60 Fundamental Theorem, again

61 You think… When you see… Integrate

62 1. Estimation: LRAM RRAM (Riemann Sums) MRAM Trapezoid 2. Geometry 3.Antiderivative FTC 4. Calculator Methods for Integration

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

64 Area using Riemann sums

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

66 Solve the differential equation...

67 You think… When you see… Meaning of

68 Meaning of the integral of f(t) from a to x

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

70

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

72 Horizontal tangent line

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

74 Vertical tangent line to f(x)

75 You think… When you see… Find the minimum acceleration given v(t)

76 Given v(t), find minimum acceleration

77 You think… When you see… Approximate the value f(c) of by using the tangent line to f at x = a

78 Approximate f(c) using tangent line to f(x) at x = 0

79 You think… When you see… Find the exact value f(c)

80

81 You think… When you see… Given the value of F(a) and the fact that the anti-derivative of f is F, find F(b)

82 FTC

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

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

85 You think… When you see… Given a graph of find where f(x) is increasing

86 Given a graph of f ‘(x), find where f(x) is increasing

87 You think… When you see… Given a chart of x and f(x) on selected values between a and b, estimate where c is between a and b.

88 MVT

89 You think… When you see… Given, draw a slope field

90 Draw a slope field of dy/dx

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

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

93 You think… When you see… Volume of Revolution

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