2.2 Defining the Derivative of a Function and Using Derivative Notation
- Syllabus
- 2020
- Topic
- 2.2
- Level
- —
Learning objectives
—CHA-2.B—Represent the derivative of a function as the limit of a difference quotient—Topic 2.2• CHA-2.B Represent the derivative of a function as the limit of a difference quotient.• CHA-2.B.2 The derivative of f is the function whose value at x is lim h→0 (f(x + h) − f(x))/h, provided this limit exists.• CHA-2.B.3 For y = f(x), notations for the derivative include dy/dx, f′(x), and y′.• CHA-2.B.4 The derivative can be represented graphically, numerically, analytically, and verbally.• 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.C—Determine the equation of a line tangent to a curve at a given point• CHA-2.C Determine the equation of a line tangent to a curve at a given point.• CHA-2.C.1 The derivative of a function at a point is the slope of the line tangent to a graph of the function at that point.• 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—Topic 2.2
- CHA-2.B Represent the derivative of a function as the limit of a difference quotient.
- CHA-2.B.2 The derivative of f is the function whose value at x is lim h→0 (f(x + h) − f(x))/h, provided this limit exists.
- CHA-2.B.3 For y = f(x), notations for the derivative include dy/dx, f′(x), and y′.
- CHA-2.B.4 The derivative can be represented graphically, numerically, analytically, and verbally.
- 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.C—Determine the equation of a line tangent to a curve at a given point
- CHA-2.C Determine the equation of a line tangent to a curve at a given point.
- CHA-2.C.1 The derivative of a function at a point is the slope of the line tangent to a graph of the function at that point.
- 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.