Section

Topics

Suggested Problems

3.6

• Derivative of ln(x)
• Using this with the Chain Rule
• Logarithmic differentiation

• 3, 7, 10, 16, 31
• 4, 8, 12, 13, 19, 26
• 37, 38, 41, 43, 45

3.7

• Derivative = rate of change
• Position, velocity, acceleration
• Rate of population growth
• Marginal cost

• 13, 14, 18, 19, 21
• 1, 3, 5, 9, 10
• 23, 24
• 29, 30

3.8

• Growth proportional to quantity
• Population models
• Radioactive decay
• Newton’s Law of Cooling

• 12, 17, 20
• 2, 3, 5,
• 8, 9, 10
• 13, 14, 15

3.9

• Related quantities have related rates of change

• 2, 5, 10, 11, 14, 19, 20, 25, 31

4.1

• Absolute maximums and minimums
• Local (relative) maximums and minimums
• Finding local extrema (Fermat’s Theorem)
• Finding absolute extrema (The Extreme Value Theorem)

• 1, 5, 7, 8
• 5, 7, 8
• 29, 30, 34, 38
• 18, 19, 23, 24, 25, 47, 48, 50, 53, 57

4.2

• Conditions for the Mean Value Theorem
• Conclusion of the Mean Value Theorem

• 11, 12, 13, 14, 15
• 7, 8, 11, 12, 13, 14

4.3

• Increasing and decreasing functions, and the first derivative
• Concavity and the second derivative
  
• First and second derivative tests

• 5, 69, 10, 13, 15, 25, 35, 39, 44
• 10, 13, 15, 25, 35, 39, 44
• 5, 6, 19, 20

4.4

• Recognizing indeterminate forms:
  0/0, ∞/∞, ∞ - ∞, 00, 0∞, 1∞
• Using L’Hopital’s Rule

• 1 – 4
• 5, 7, 9, 10, 11, 12, 15, 16, 17, 29, 32, 39, 40, 42, 47, 53, 55, 59

4.5

• Domain, intercepts, asymptotes, symmetry
• Increasing vs. decreasing; 1st derivative
• Local extrema
• Concavity; the 2nd derivative
• Inflection points

• 2, 4, 5, 11, 12, 13, 14, 19, 20, 24, 31, 32, 33, 37, 39, 42, 47