Download presentation

Presentation is loading. Please wait.

Published byAllison Scott Modified over 2 years ago

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… Show that f(x) is even

8
8 Even function

9
9 You think… When you see… Show that f(x) is odd

10
10 Odd function

11
11 You think… When you see… Find the interval where f(x) is increasing

12
12 f(x) increasing

13
13 You think… When you see… Find the interval where the slope of f (x) is increasing

14
14 Slope of f (x) is increasing

15
15 You think… When you see… Find the minimum value of a function

16
16 Local Minimum value of a function

17
17 You think… When you see… Find critical numbers

18
18 Find critical numbers

19
19 You think… When you see… Find inflection points

20
20 Find inflection points

21
21 You think… When you see… Show that exists

22
22 Show exists Show that

23
23 You think… When you see… Show that f(x) is continuous

24
24. f(x) is continuous

25
25 You think… When you see… Show that f(x) is differentiable at x = a

26
26 f(x) is differentiable

27
27 You think… When you see… Find vertical asymptotes of f(x)

28
28 Find vertical asymptotes of f(x) Factor/cancel f(x) Set denominator = 0

29
29 You think… When you see… Find horizontal asymptotes of f(x)

30
30 Find horizontal asymptotes of f(x)

31
31 You think… When you see… Find the average rate of change of f(x) at [a, b]

32
32 Average rate of change of f(x) Find f (b) - f ( a) b - a

33
33 You think… When you see… Find the instantaneous rate of change of f(x) at x = a

34
34 Instantaneous rate of change of f(x) Find f ( a)

35
35 You think… When you see…

36
36 Average value of the function

37
37 You think… When you see… Find the absolute maximum of f(x) on [a, b]

38
38 Find the absolute maximum of f(x)

39
39 You think… When you see… Show that a piecewise function is differentiable at the point a where the function rule splits

40
40 Show a piecewise function is differentiable at x=a

41
41 You think… When you see… Given s(t) (position function), find v(t)

42
42 Given position s(t), find v(t)

43
43 You think… When you see… Given v(t), find how far a particle travels on [a, b]

44
44 Given v(t), find how far a particle travels on [a,b]

45
45 You think… When you see… Find the average velocity of a particle on [ a, b ]

46
46 Find the average rate of change on [a,b]

47
47 You think… When you see… Given v(t), determine if a particle is speeding up at t = k

48
48 Given v(t), determine if the particle is speeding up at t=k

49
49 You think… When you see… Given v(t) and s(0), find s(t)

50
50 Given v(t) and s(0), find s(t)

51
51 You think… When you see… Show that the Mean Value Theorem holds on [a, b]

52
52 Show that the MVT holds on [a,b]

53
53 You think… When you see… Show that Rolles Theorem holds on [a, b]

54
54 Show that Rolles Theorem holds on [a,b]

55
55 You think… When you see… Find the domain of f(x)

56
56 Find the domain of f(x)

57
57 You think… When you see… Find the range of f(x) on [a, b]

58
58 Find the range of f(x) on [a,b]

59
59 You think… When you see… Find the range of f(x) on

60
60 Find the range of f(x) on

61
61 You think… When you see… Find f (x) by definition

62
62 Find f ( x) by definition

63
63 You think… When you see… Find the derivative of the inverse of f(x) at x = a

64
64 Derivative of the inverse of f(x) at x=a

65
65 You think… When you see… y is increasing proportionally to y

66
66 y is increasing proportionally to y. y is increasing proportionally to y

67
67 You think… When you see… Find the line x = c that divides the area under f(x) on [ a, b ] into two equal areas

68
68 Find the x=c so the area under f(x) is divided equally

69
69 You think… When you see…

70
70 Fundamental Theorem

71
71 You think… When you see…

72
72 Fundamental Theorem, again Given:

73
73 You think… When you see… The rate of change of population is …

74
74 Rate of change of a population

75
75 You think… When you see… The line y = mx + b is tangent to f(x) at (a, b)

76
76 y = mx+b is tangent to f(x) at (a,b). y = mx+b is tangent to f(x) at (a,b)

77
77 You think… When you see… Integrate

78
78 1. Estimation: LRAM RRAM (Riemann Sums) MRAM Trapezoid 2. Geometry 3.Antiderivative Straight Forward Substitution Rewrite (Simplify) Methods for Integration

79
79 You think… When you see… Find area using Left Riemann sums

80
80 Area using Left Riemann sums

81
81 You think… When you see… Find area using Right Riemann sums

82
82 Area using Right Riemann sums

83
83 You think… When you see… Find area using Midpoint rectangles

84
84 Area using midpoint rectangles

85
85 You think… When you see… Find area using trapezoids

86
86 Area using trapezoids

87
87 You think… When you see… Solve the differential equation …

88
88 Solve the differential equation...

89
89 You think… When you see… Meaning of

90
90 Meaning of the integral of f(t) from a to x

91
91 You think… When you see… Given a base, cross sections perpendicular to the x-axis that are squares

92
92 Semi-circular cross sections perpendicular to the x-axis

93
93 You think… When you see… Find where the tangent line to f(x) is horizontal

94
94 Horizontal tangent line

95
95 You think… When you see… Find where the tangent line to f(x) is vertical

96
96 Vertical tangent line to f(x)

97
97 You think… When you see… Find the minimum acceleration given v(t)

98
98 Given v(t), find minimum acceleration

99
99 You think… When you see… Approximate the value f(0.1) of by using the tangent line to f at x = a

100
100 Approximate f(0.1) using tangent line to f(x) at x = 0

101
101 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)

102
102 Given F(a) and the that the anti-derivative of f is F, find F(b)

103
103 You think… When you see… Find the derivative of f(g(x))

104
104 Find the derivative of f(g(x)) Think... Chain Rule

105
105 You think… When you see… Given, find

106
106 Given area under a curve and vertical shift, find the new area under the curve

107
107 You think… When you see… Given a graph of find where f(x) is increasing

108
108 Given a graph of f (x), find where f(x) is increasing

109
109 You think… When you see… Given v(t) and s(0), find the greatest distance from the origin of a particle on [ a, b ]

110
110 Given v(t) and s(0), find the greatest distance from the origin of a particle on [ a, b ]

111
111 When you see… Given a water tank with g gallons initially being filled at the rate of F(t) gallons/min and emptied at the rate of E(t) gallons/min on, find

112
112 You think… a)the amount of water in the tank at m minutes

113
113

114
114 Amount of water in the tank at t minutes initial gallons

115
115 You think… b) the rate the water amount is changing at m

116
116 Rate the amount of water is changing at t = m

117
117 You think… c) the time when the water is at a minimum

118
118 The time when the water is at a minimum

119
119 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.

120
120

121
121 You think… When you see… Given, draw a slope field

122
122 Draw a slope field of dy/dx

123
123 You think… When you see… Find the area between curves f(x) and g(x) on [a,b]

124
124 Area between f(x) and g(x) on [a,b]

125
125 You think… When you see… Find the volume if the area between the curves f(x) and g(x) with a representative rectangle perpendicular to the axis of rotation

126
126 Volume generated by rotating area between f(x) and g(x) with a representative rectangle perpendicular to the axis of rotation

127
127 You think… When you see… Find the volume if the area between the curves f(x) and g(x) with a representative rectangle parallel to the axis of rotation

128
128 Volume generated by rotating area between f(x) and g(x) with a representative rectangle parallel to the axis of rotation Remember: Always... Big - small

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google