In the previous chapter, we learned how to differentiate. In this chapter, we will learn how to use differentiation to
  • study the motion of an object in a straight line,
  • calculate the rate at which a quantity is changing if the rates of change of other quantities are given,
  • locate the key features of graphs,
  • find the maximum and minimum values of a function,
  • evaluate indeterminate limits,
  • find the optimum value of a variable in many practical problems,
  • etc.
Specifically, in this chapter, we will talk about
  1. Tangents and Normals
  2. Rectilinear Motion
  3. Related Rates
  4. Extreme Values of Functions
  5. Rolle’s Theorem
  6. The Mean-Value Theorem
  7. Increasing and Decreasing Functions
  8. Concavity and Points of Inflection
  9. First Derivative Test for Local Extrema
  10. Second Derivative Test for Local Extrema
  11. L’Hôpital’s Rule for Indeterminate Limits
  12. Curve Sketching
  13. Optimization