September 11, 2014

In this, the second section of the course, the topics include:

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.

Derivative at a point

• 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.

Derivative as a function

• Corresponding characteristics of graphs of ƒ and ƒ’.

• Relationship between the increasing and decreasing behavior of ƒ and the sign of ƒ’.

• The Mean Value Theorem and its geometric interpretation.

• Equations involving derivatives. Verbal descriptions are translated into equations

involving derivatives and vice versa.

Second derivatives

• Corresponding characteristics of the graphs of ƒ, ƒ’, and ƒ?’’.

• Relationship between the concavity of ƒ and the sign of ƒ?’’.

• Points of inflection as places where concavity changes.

- Mathematics > General
- Mathematics > Calculus

- Grade 11
- Grade 12