1. §2.7. Derivatives

2. Tangents

6. Velocities

8. Rates of change
Problem: Suppose y is a function of x and y = f(x). Find
the instantaneous rate of change of y with respect to x.
Solution: If x changes from x1 to x2, then the change in
x is called the increment of x and denoted by
x = x2 – x1 and the corresponding change in y is called
the increment of y and is given by y = f(x2) – f(x1).
The average rate of change of y with respect to x over
the interval [x1, x2] is given by
y/x = [f(x2) – f(x1)]/(x2 – x1)

10. Derivatives