1. Applications of the Derivative
Chapter 4
Applications of
the Derivative

2. 4.1
Maxima and Minima

4. Figure 4.1

5. Figure 4.2 (a & b)

6. Figure 4.2 (c & d)

7. Figure 4.3

9. Figure 4.4

10. Figure 4.5

12. Figure 4.6

13. Figure 4.7

16. Figure 4.8 (a & b)

17. Figure 4.9 (a)

18. Figure 4.9 (b)

19. Figure 4.10

21. Figure 4.11

22. Figure 4.12

23. What Derivatives Tell Us
4.2
What Derivatives Tell Us

25. Figure 4.13 (a & b)

26. Figure 4.14

28. Figure 4.15

29. Figure 4.16

30. Figure 4.17

31. Figure 4.18

32. Figure 4.19 (a)

33. Figure 4.19 (b)

34. Figure 4.20

36. Figure 4.21

37. Figure 4.22

38. Figure 4.23

39. Figure 4.24

41. Figure 4.25

42. Figure 4.26

43. Figure 4.27

46. Figure 4.28 (a & b)

47. Figure 4.28 (c & d)

48. Figure 4.29 (a)

49. Figure 4.29 (b)

50. Figure 4.30

51. Figure 4.31

52. Figure 4.32

54. Figure 4.33 (a)

55. Figure 4.33 (b)

56. Figure 4.34

57. Figure 4.35

58. Figure 4.36

59. 4.3
Graphing Functions

60. Figure 4.37 (a)

61. Figure 4.37 (b)

62. continued…

63. Graphing Guideline for y = f (x) (continued)

64. Figure 4.38

65. Figure 4.39

66. Figure 4.40

67. Figure 4.41

68. Figure 4.42

69. Figure 4.43

70. Table 4.1

71. Figure 4.44

72. Figure 4.45

73. Figure 4.46

74. Figure 4.47

75. Table 4.2

76. Figure 4.48

77. Figure 4.49

78. Optimization Problems
4.4
Optimization Problems

79. Table 4.3

80. Figure 4.50

81. Figure 4.51

82. Figure 4.52

83. Figure 4.53

84. Figure 4.54

86. Figure 4.55

87. Figure 4.56

88. Figure 4.57

89. Figure 4.58 (a)

90. Figure 4.58 (b)

91. Linear Approximation and Differentials
4.5
Linear Approximation
and Differentials

92. Figure 4.59 (a & b)

93. Figure 4.60

95. Figure 4.61

96. Table 4.4

97. Figure 4.62

98. Figure 4.63 (a)

99. Figure 4.63 (b)

100. Figure 4.64 (a)

101. Figure 4.64 (b)

102. Figure 4.65

106. Figure 4.66

107. 4.6
Mean Value Theorem

108. Figure 4.67

110. Figure 4.68

111. Figure 4.69

112. Figure 4.70

114. Figure 4.71

115. Figure 4.72

116. Figure 4.73

120. 4.7
L’Hôpital’s Rule

122. Figure 4.74

123. Figure 4.75

126. Figure 4.76

127. Figure 4.77

129. Figure 4.78

130. Figure 4.79

132. 4.8
Newton’s Method

133. Figure 4.80 (a)

134. Figure 4.80 (b)

135. Figure 4.80 (c)

136. Figure 4.81

138. Figure 4.82

139. Table 4.5

140. Figure 4.83 (1 of 2)

141. Figure 4.83 (2 of 2)

142. Figure 4.84

143. Table 4.6

144. Figure 4.85

145. Table 4.7

146. Table 4.8

147. Figure 4.86

148. Figure 4.87

149. Figure 4.88

150. 4.9
Antiderivatives

153. Figure 4.89

156. Table 4.9

157. Table 4.10

158. Figure 4.90

160. Figure 4.91

161. Figure 4.92

162. Figure 4.93

163. Figure 4.94