Day 17 - Basic Differentiation Rules - 09.10.14

Bell Ringer

    1. Find f(x + h), if f(x) = x3

      1. x3 + 2hx2 + 2h2x + xh2 + h3

      2. x3 + 3hx2 + 3h2x + h3

      3. x3 + hx2 + 2h2x + xh2 + h3

      4. x3 + hx2 + 2hx2 +2h2x + xh2

      5. none of the above

    2. Find the derivative of the following function: f(x) = x3 + 2x

      1. 3x2 + 2

      2. 3x2 - 2

      3. 3x2

      4. -3x2 + 2

      5. none of the above

    3. Find the slope of the tangent line at (1, 1) of the following function: f(x) = x1/2

      1. 1 / (2x1/2)

      2. 1 / 2

      3. -1 / 2

      4. 2x1/2

      5. none of the above

    4. Find f’(t) and f’(3) based on f(t) = 2 / t

      1. f’(t) = 2 / t2 and f’(3) = 2 / 9

      2. f’(t) = -2 / t2 and f’(3) = 2 / 9

      3. f’(t) = -2 / t2 and f’(3) = -2 / 9

      4. f’(t) = 2 / t2 and f’(3) = -2 / 9

      5. none of the above

    5. What are the points in which the f(x) has a horizontal tangent line? f(x) = x3 - 3x

      1. (1, 2)

      2. (-1, 2)

      3. (0, 0)

      4. (1, -1)

      5. none of the above
    Review
    • Secant vs. Tangent Line
      • Slope
    • Definition of Derivative
      • Importance of Derivative
        • What does it allow us to do?
    • Drawing a Tangent Line on a Graph
    Lesson
    • Basic Differentiation Rules
      • Constant Rule
      • Power Rule
      • Sum and Difference Rule
    • Practice
      • page 115 #1
      • Checkpoint #1
        • page 115 #2
      • page 115 #3-17 (odds)
      • Checkpoint #2
        • page 115 #10
      • Checkpoint #3
        • page 115 #18
      • page 115 #39-49 (odds)
      • Checkpoint #4
        • page 115 #50
      • Checkpoint #5
        • page 115 #52
      • page 116 #59 and 61
      • Checkpoint #6
        • page 116 #62
    • Work on Student-led Lessons!
    Exit Ticket
    • Exit TIcket will be posted on the board in class.
    Lesson Objective(s)
    • What rules can be created for finding the derivative involving:
      • constants
      • powers
      • sum and differences
    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.
    Mathematical Practice(s)
    • #1 - Make sense of problems and persevere in solving them
    • #2 - Reason abstractly and quantitatively
    • #3 - Construct viable arguments and critique the reasoning of others
    • #4 - Model with mathematics
    • #8 - Look for and express regularity in repeated reasoning

    In-class Help Request