Chapter 1 Outline and Links
**Nearly all these topics can also be found by searching at: https://www.khanacademy.org/math.
0.1 Functions and Their Graphs
- What is the definition of a function? What does it mean to evaluate a function?
- What is interval notation? How does it relate to inequality notation?
- What is the domain of a function? What two types of functions have constraints on the domain?
- What are the laws of exponents?
1.1 The Slope of a Straight Line
- What are the three forms of linear equations?
- What is the slope formula?
1.2 The Slope of a Curve at a Point
- What line is used to find the slope of a curve at a point?
1.3 The Derivative and Limits
- How does the derivative relate to the slope of the tangent line to the curve?
- What is the Power Rule for derivatives?
- What is the process for finding the equation of a tangent line to a curve?
1.6 Some Rules for Differentiation
- What is the Constant Multiple Rule?
- What is the Sum Rule?
- https://www.youtube.com/watch?v=hIlnBWb3N8M (don’t bother with the proof)
- What is the General Power Rule (Chain Rule)?
1.7 More about Derivatives
- Derivatives with respect to a specific variable will be covered in class.
- What is the second derivative of a function? How is it found?
- Be familiar with the various notations for the derivative.
- Derivative as a rate of change will be covered in class.
- How are the cost, revenue, and profit functions related? How are marginal cost/revenue/profit functions found? What does marginal cost/revenue/profit represent?
1.8 The Derivative as a Rate of Change
- What is the average rate of change? How is it calculated? What is the instantaneous rate of change? How is it calculated?
- How is velocity related to position? How is acceleration related to velocity? How are derivatives used to find the velocity and acceleration functions?
- Units for rates of change will be covered in class.