Day 20 - Product/Quotient Rule - 09.14.15

Update
Bell Ringer

  1. Find the derivative of the following:

    5. none of the above

  2. Find the second derivative (derivative of the derivative) of the following:

    5. none of the above

  3. Find the point(s) at which the following function has a horizontal tangent line:

    5. none of the above

  4. Find the derivative of the following function using the Product Rule:

    5. none of the above

  5. Find the derivative of the following function:

    5. none of the above
Review
  • Pre-calculus
    • Slope
    • Equation of a Line
    • Secant Line vs. Tangent Line (video)
  • Tangent Line
    • How can the slope of one point be found?
    • Finding the derivative of polynomials using limits (example)
  • Basic Differentiation Rules
    • How can derivatives be calculated using basic differentiation rules?
  • Product Rule/Quotient Rule
    • How can derivatives of the product/quotient of functions be calculated
Lesson
Exit Ticket
  • Posted on the board at the end of the block.
Homework
  • WNQ the following:

Lesson Objectives
  • How can the Product Rule and Quotient Rule be used to find derivatives?

In-Class Help Requests



Standard(s)
  • APC.5
    • Investigate derivatives presented in graphic, numerical, and analytic contexts and the relationship between continuity and differentiability.
      • The derivative will be defined as the limit of the difference quotient and interpreted as an instantaneous rate of change.
  • APC.6
    • ​The student will investigate the derivative at a point on a curve.
      • Includes:
        • finding the slope of a curve at a point, including points at which the tangent is vertical and points at which there are no tangents
        • using local linear approximation to find the slope of a tangent line to a curve at the point
        • ​defining instantaneous rate of change as the limit of average rate of change
        • approximating rate of change from graphs and tables of values.