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

2. Sec 2.7: Derivative and Rates of Change
Def:
The difference quotient of ƒ at x0 with increment h.
The derivative of a function ƒ at a point x0
Def:
The slope of the secant to the curve f(x) at the point x0 is
Def:
The slope of the tangent to the curve f(x) at the point x0 is
Def:
Def:
average velocity
Def:
instantaneous velocity
Term-111

3. Sec 3.1: Tangents and the Derivative at a Point
Term-111

4. Sec 2.7: Derivative and Rates of Change
Def:
The difference quotient of ƒ at x0 with increment h.
The derivative of a function ƒ at a point x0
Def:
The slope of the secant to the curve f(x) at the point x0 is
Def:
The slope of the tangent to the curve f(x) at the point x0 is
Def:
Def:
average velocity
Def:
instantaneous velocity
Def:
average rate of change
Def:
instantaneous rate of change

5. Sec 2.7: Derivative and Rates of Change
Suppose y is a quantity that depends on another quantity x. Thus y is a function of x and we write y = f(x).
Temperature in Dhahran T depends on time t
If x changes from x1 to x2 , then the change in x
(also called the increment of x)
Give an example for quantity that depends on another
and the corresponding change in is
The instantaneous rate of change of ƒ with respect to x at
The average rate of change of ƒ with respect to x over the interval
Term 102
Term 102
Term 121