Day 18 - Rates of Change, Position Function, Trig Derivatives - 09.11.14

Bell Ringer
      1. What are the points in which the f(x) has a horizontal tangent line? f(x) = 4x3 - 48x

        1. (2, -64)

        2. (2, 64)

        3. (2, -64) and (-2, 64)

        4. (2, 0) and (-2, 0)

        5. none of the above

      2. Using the following position function, find the average velocity over the period of [1, 2]. s(t) = -16t2 + 100

        1. -48

        2. -40

        3. -32

        4. -30

        5. none of the above

      3. Using the function in #2, find the instantaneous velocity at t = 2.

        1. -64

        2. -40

        3. -32

        4. -30

        5. none of the above

      4. Using the function in #2, find the instantaneous acceleration at t = 2.

        1. -64

        2. -40

        3. -32

        4. -30

        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
      • Basic Differentiation Rules
        • Constant Rule
        • Power Rule
        • Sum and Difference Rule

      Lesson
      • Rates of Change
        • Position Function
      • Sine and Cosine Derivatives
      • Practice (Section 2.2)
        • Checkpoint #1
          • page 115 #20, #22, #24
        • Checkpoint #2
          • page 115 #36 and #38
        • Checkpoint #3
          • page 116 #54 and #64
        • Checkpoint #4
          • page 116 #78 and #80
      • 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:
        • sine and cosine functions
        • rates of change

      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