2.1 Defining Average and Instantaneous Rates of Change at a Point
- Syllabus
- 2020
- Topic
- 2.1
- Level
- —
Learning objectives
—CHA-2.A—Determine average rates of change using difference quotients• CHA-2.A Determine average rates of change using difference quotients.• CHA-2.A.1 The difference quotients (f(a + h) − f(a))/h and (f(x) − f(a))/(x − a) express the average rate of change of a function over an interval.• Enduring understanding CHA-2: Derivatives allow us to determine rates of change at an instant by applying limits to knowledge about rates of change over intervals.—CHA-2.B—Represent the derivative of a function as the limit of a difference quotient• CHA-2.B Represent the derivative of a function as the limit of a difference quotient.• CHA-2.B.1 The instantaneous rate of change of a function at x = a can be expressed by lim h→0 (f(a + h) − f(a))/h or lim x→a (f(x) − f(a))/(x − a), provided the limit exists. These are equivalent forms of the definition of the derivative and are denoted f′(a).• Enduring understanding CHA-2: Derivatives allow us to determine rates of change at an instant by applying limits to knowledge about rates of change over intervals.
CHA-2.A—Determine average rates of change using difference quotients
- CHA-2.A Determine average rates of change using difference quotients.
- CHA-2.A.1 The difference quotients (f(a + h) − f(a))/h and (f(x) − f(a))/(x − a) express the average rate of change of a function over an interval.
- Enduring understanding CHA-2: Derivatives allow us to determine rates of change at an instant by applying limits to knowledge about rates of change over intervals.
CHA-2.B—Represent the derivative of a function as the limit of a difference quotient
- CHA-2.B Represent the derivative of a function as the limit of a difference quotient.
- CHA-2.B.1 The instantaneous rate of change of a function at x = a can be expressed by lim h→0 (f(a + h) − f(a))/h or lim x→a (f(x) − f(a))/(x − a), provided the limit exists. These are equivalent forms of the definition of the derivative and are denoted f′(a).
- Enduring understanding CHA-2: Derivatives allow us to determine rates of change at an instant by applying limits to knowledge about rates of change over intervals.