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

2. 4.1
Maxima and Minima

3. 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

26. Figure 4.14

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

35. Figure 4.20

36. Figure 4.21

37. Figure 4.22

38. Figure 4.23

40. Figure 4.24

41. Figure 4.25

42. Figure 4.26

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)

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

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

91. Figure 4.57

92. Table 4.4

93. Figure 4.58

94. Figure 4.59

98. Figure 4.60

99. 4.6
Mean Value Theorem

100. Figure 4.61

102. Figure 4.62

103. Figure 4.63

104. Figure 4.64

106. Figure 4.65

107. Figure 4.66

108. Figure 4.67

112. 4.7
L’Hôpital’s Rule

114. Figure 4.68

115. Figure 4.69

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

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

138. Figure 4.79

141. Table 4.9

142. Figure 4.80

144. Figure 4.81

145. Figure 4.82

146. Figure 4.83

147. Figure 4.84