Derivatives

D.1 - Defining the Derivative

Objectives

• Recognize the meaning of the tangent to a curve at a point.
• Calculate the slope of a tangent line.
• Identify the derivative as the limit of a difference quotient.
• Calculate the derivative of a given function at a point.

Activities

• Video D1A - The difference quotient and definition of derivative
• Video D1B - Derivative Notation and example problem
• Reading - Openstax Section 3.1 Pay special attention to examples 3.1, 3.2, 3.3, 3.5, and 3.6. The section on velocity and rates of change is nice. It can be summarized as: The derivative of position as a function of time is velocity. Ignore example 3.7, but try checkpoint 3.4.
• Section 3.1 Recommended Practice Problems
  • 11, 14, 16, 20, 22, 26, 29
  • Number 20 Worked out

D.2 - The Derivative as a Function

Objectives

• Define the derivative function of a given function.
• Graph a derivative function from the graph of a given function.
• Describe three conditions for when a function does not have a derivative.
• Explain the meaning of a higher-order derivative

Activities

• Video D2A - The derivative of a function - Sketching and finding, and Leibniz Notation.
• Video D2B - Higher order derivatives and nondifferentiable functions
• Reading Openstax section 3.2 - Example 3.11 is a good reminder of conjugates,
• Section 3.2 Recommended Practice Problems
  • 54, 55, 57, 58, 64, 65, 67, 68,

D.3 - Differentiation Rules