INTRODUCING THE DERIVATIVE

• Differentiability and f '(a)
• Derivative at a Point: A Sample Problem
• Differentiability: More Examples
• Derivatives of a Function
• Notation: Lagrange and Leibniz

• Rate of Change
  • Inflating a Spherical Balloon
    • Volume as a Function of Time
    • Volume as a Function of Radius
    • Equipment Check
• Tangent Lines
  • Secant Lines: Why is the Slope Equal to f '(a)?
• Differentiability vs. Continuity

The Lesson introduces the derivatives of a function and examines their meaning.

Expected Study Time

You will need two to three hours to go through this Lesson. You may wish to return to the Lesson later for help in completing Practice problems.

Objectives

• Use the definition of differentiability.
• Compare continuity and differentiability.
• Use the various notations for the derivatives of a function.
• Interpret the values of the derivative of a function.