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

- Tangents and Normals
- Rectilinear Motion
- Related Rates
- Extreme Values of Functions
- Rolle’s Theorem
- The Mean-Value Theorem
- Increasing and Decreasing Functions
- Concavity and Points of Inflection
- First Derivative Test for Local Extrema
- Second Derivative Test for Local Extrema
- L’Hôpital’s Rule for Indeterminate Limits
- Curve Sketching
- Optimization