Applications of the Derivative Chapter 4 Applications of the Derivative

4.1 Maxima and Minima

Figure 4.1

Figure 4.2 (a & b)

Figure 4.2 (c & d)

Figure 4.3

Figure 4.4

Figure 4.5

Figure 4.6

Figure 4.7

Figure 4.8 (a & b)

Figure 4.9 (a)

Figure 4.9 (b)

Figure 4.10

Figure 4.11

Figure 4.12

What Derivatives Tell Us 4.2 What Derivatives Tell Us

Figure 4.13

Figure 4.14

Figure 4.15

Figure 4.16

Figure 4.17

Figure 4.18 (a)

Figure 4.18 (b)

Figure 4.19

Figure 4.20

Figure 4.21

Figure 4.22

Figure 4.23

Figure 4.24

Figure 4.25

Figure 4.26

Figure 4.27 (a & b)

Figure 4.27 (c & d)

Figure 4.28 (a)

Figure 4.28 (b)

Figure 4.29

Figure 4.30

Figure 4.31 (a)

Figure 4.31 (b)

Figure 4.32

Figure 4.33

Figure 4.34

4.3 Graphing Functions

Figure 4.35 (a)

Figure 4.35 (b)

continued…

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

Figure 4.36

Figure 4.37

Figure 4.38

Figure 4.39

Figure 4.40

Figure 4.41

Table 4.1

Figure 4.42

Figure 4.43

Table 4.2

Figure 4.44

Figure 4.45

Optimization Problems 4.4 Optimization Problems

Table 4.3

Figure 4.46

Figure 4.47

Figure 4.48

Figure 4.49

Figure 4.50

Figure 4.51

Figure 4.52

Figure 4.53

Figure 4.54 (a)

Figure 4.54 (b)

Linear Approximation and Differentials 4.5 Linear Approximation and Differentials

Figure 4.55 (a & b)

Figure 4.56

Figure 4.57

Table 4.4

Figure 4.58

Figure 4.59

Figure 4.60

4.6 Mean Value Theorem

Figure 4.61

Figure 4.62

Figure 4.63

Figure 4.64

Figure 4.65

Figure 4.66

Figure 4.67

4.7 L’Hôpital’s Rule

Figure 4.68

Figure 4.69

4.8 Newton’s Method

Figure 4.70 (a)

Figure 4.70 (b)

Figure 4.70 (c)

Figure 4.71

Figure 4.72

Table 4.5

Figure 4.73 (1 of 2)

Figure 4.73 (2 of 2)

Figure 4.74

Table 4.6

Figure 4.75

Table 4.7

Table 4.8

Figure 4.76

Figure 4.77

Figure 4.78

4.9 Antiderivatives

Figure 4.79

Table 4.9

Figure 4.80

Figure 4.81

Figure 4.82

Figure 4.83

Figure 4.84