The Derivative
What is a Limit?
When does a limit exist?
Evaluating Limits
Limits and Infinity
Continuity Intermediate Value Theorem
Tangent Lines
The Difference Quotient
Definition of the Derivative
The Derivative at a Point
Calculus Grapher
Chapter 2 Study Guide (MS Word)
When does a limit exist?
Evaluating Limits
Limits and Infinity
Continuity Intermediate Value Theorem
Tangent Lines
The Difference Quotient
Definition of the Derivative
The Derivative at a Point
Calculus Grapher
Chapter 2 Study Guide (MS Word)
AP Calculus (BC) Topics
II. Derivatives
A. Concept of the derivative.
II. Derivatives
A. Concept of the derivative.
- Derivative presented graphically, numerically, and analytically.
- Derivative interpreted as an instantaneous rate of change.
- Derivative defined as the limit of the difference quotient.
- Relationship between differentiability and continuity.
- Slope of a curve at a point. Examples are emphasized, including points at which there are vertical tangents and points at which there are no tangents.
- Tangent line to a curve at a point and local linear approximation.
- Instantaneous rate of change as the limit of average rate of change.
- Approximate rate of change from graphs and tables of values.
- Corresponding characteristics of graphs of f and f'.
- Relationship between the increasing and decreasing behavior of f and the sign of f'.
- The Mean Value Theorem and its geometric consequences.
- Equations involving derivatives. Verbal descriptions are translated into equations involving derivatives and vice versa.
- Corresponding characteristics of the graphs of f, f', and f''.
- Relationships between the concavity of f and the sign of f''.
- Points of inflection as places where concavity changes.