2 Modeling Rates of Change

• 2.1 Introduction to the Issues

  2.1.1 Average Speed
  2.1.2 The Meaning of Constant Acceleration
  2.1.3 Hypotheses and Open Questions
  2.1.4 The Distance Function is Quadratic
  2.1.5 Average Rate of Change
  2.1.6 An Agenda for Future Work
  

• 2.2 The Legacy of Galileo, Newton, and Leibniz
• 2.3 Limits of Functions
• 2.4 Limits at Infinity
• 2.5 Continuity
• 2.6 Tangent Lines and Their Slopes
• 2.7 The Derivative
• 2.8 Differentiation Rules
• 2.9 Derivatives of the Trigonometric Functions
• 2.10 The Mean Value Theorem
• 2.11 Implicit Differentiation
• 2.12 Derivatives of Exponential and Logarithm Functions
• 2.13 Newton’s Method
• 2.14 Linear Approximations
• 2.15 Antiderivatives and Initial Value Problems
• 2.16 Velocity and Acceleration
• 2.17 Related Rates
• 2.18 Case Study: Torricelli’s Law