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Applications of the Derivative

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1 Applications of the Derivative
Chapter 4 Applications of the Derivative

2 4.1 Maxima and Minima

3 Figure 4.1

4

5 Figure 4.2 (a & b)

6 Figure 4.2 (c & d)

7 Figure 4.3

8

9 Figure 4.4

10 Figure 4.5

11

12 Figure 4.6

13 Figure 4.7

14

15

16 Figure 4.8 (a & b)

17 Figure 4.9 (a)

18 Figure 4.9 (b)

19 Figure 4.10

20

21 Figure 4.11

22 Figure 4.12

23 What Derivatives Tell Us
4.2 What Derivatives Tell Us

24

25 Figure 4.13

26 Figure 4.14

27

28 Figure 4.15

29 Figure 4.16

30 Figure 4.17

31 Figure 4.18 (a)

32 Figure 4.18 (b)

33 Figure 4.19

34

35 Figure 4.20

36 Figure 4.21

37 Figure 4.22

38 Figure 4.23

39

40 Figure 4.24

41 Figure 4.25

42 Figure 4.26

43

44

45 Figure 4.27 (a & b)

46 Figure 4.27 (c & d)

47 Figure 4.28 (a)

48 Figure 4.28 (b)

49 Figure 4.29

50 Figure 4.30

51 Figure 4.31 (a)

52 Figure 4.31 (b)

53

54 Figure 4.32

55 Figure 4.33

56 Figure 4.34

57 4.3 Graphing Functions

58 Figure 4.35 (a)

59 Figure 4.35 (b)

60 continued…

61 Graphing Guideline for y = f (x) (continued)

62 Figure 4.36

63 Figure 4.37

64 Figure 4.38

65 Figure 4.39

66 Figure 4.40

67 Figure 4.41

68 Table 4.1

69 Figure 4.42

70 Figure 4.43

71 Table 4.2

72 Figure 4.44

73 Figure 4.45

74 Optimization Problems
4.4 Optimization Problems

75 Table 4.3

76 Figure 4.46

77 Figure 4.47

78 Figure 4.48

79 Figure 4.49

80 Figure 4.50

81

82 Figure 4.51

83 Figure 4.52

84 Figure 4.53

85 Figure 4.54 (a)

86 Figure 4.54 (b)

87 Linear Approximation and Differentials
4.5 Linear Approximation and Differentials

88 Figure 4.55 (a & b)

89 Figure 4.56

90

91 Figure 4.57

92 Table 4.4

93 Figure 4.58

94 Figure 4.59

95

96

97

98 Figure 4.60

99 4.6 Mean Value Theorem

100 Figure 4.61

101

102 Figure 4.62

103 Figure 4.63

104 Figure 4.64

105

106 Figure 4.65

107 Figure 4.66

108 Figure 4.67

109

110

111

112 4.7 L’Hôpital’s Rule

113

114 Figure 4.68

115 Figure 4.69

116

117 4.8 Newton’s Method

118 Figure 4.70 (a)

119 Figure 4.70 (b)

120 Figure 4.70 (c)

121 Figure 4.71

122

123 Figure 4.72

124 Table 4.5

125 Figure 4.73 (1 of 2)

126 Figure 4.73 (2 of 2)

127 Figure 4.74

128 Table 4.6

129 Figure 4.75

130 Table 4.7

131 Table 4.8

132 Figure 4.76

133 Figure 4.77

134 Figure 4.78

135 4.9 Antiderivatives

136

137

138 Figure 4.79

139

140

141 Table 4.9

142 Figure 4.80

143

144 Figure 4.81

145 Figure 4.82

146 Figure 4.83

147 Figure 4.84


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