1. Sec 2.7: Derivative and Rates of Change
Def:
Def:
The derivative of a function ƒ at a point x0
The difference quotient of ƒ at x0 with increment h.
Example:
Example:
Find the difference quotient of ƒ at x=2 with increment h.
Find the derivative of ƒ at x=2

2. Sec 2.7: Derivative and Rates of Change
Example:
Find the derivative of ƒ at x0=2
Def:
The derivative of a function ƒ at a point x0
Example:
Find

3. Sec 2.7: Derivative and Rates of Change
Def:
The derivative of a function ƒ at a point x0
Example:
Find

4. The slope of the tangent to the curve f(x) at the point x0 is

5. Sec 2.7: Derivative and Rates of Change
Def:
Chane in x =
Chane in y =

6. Tangents and the Derivative at a Point
Def:
Def:
The average rate of change of ƒ with respect to x over the interval [a, b]
The rate of change of ƒ with respect to x at x0
The instantaneous rate of change of ƒ with respect to x at x0

7. Sec 3.1: Tangents and the Derivative at a Point
quotient
The slope of the secant
The slope of the tangent to the curve
instantaneous rate of change
Average rate of change

8. Tangents and the Derivative at a Point
quotient
The slope of the tangent to the curve
The slope of the secant
The slope of the curve
instantaneous rate of change
Average rate of change

9. Sec 3.1: Tangents and the Derivative at a Point

10. Summary slope of the secant slope of the tangent
The instantaneous rate of change
The average rate of change
average velocity
instantaneous velocity