Day 41 - Increasing and Decreasing Functions - 10.15.14

Updates
  • Quiz 7 on Friday!
    • Covers the entire new unit so far
      • Extrema
      • Rolle's Theorem
      • Mean Value Theorem
      • Increasing and Decreasing Functions
      • First Derivative Test
Bell Ringer


  • Rolle's Theorem and Mean Value Theorem

  1. Determine whether Rolle’s Theorem can be applied to the function f(x) = x2 - 4x - 5 on the closed interval [-1, 5]. If Rolle’s Theorem can be applied, find all values of c in the open interval (-1, 5) such that f’(c) = 0.

    1. Rolle’s Theorem applies; c = -2

    2. Rolle’s Theorem applies; c = 0.5

    3. Rolle’s Theorem does not apply.

    4. Rolle’s Theorem applies; c = 2

    5. both a and d

  2. Determine whether Mean Value Theorem can be applied to the function f(x) = x3 on the closed interval [0, 16]. If the Mean Value Theorem can be applied, find all numbers c in the open interval (0, 16) such that f’(c) = [f(b) - f(a)] / (b - a).

    1. MVT applies; c = 4

    2. MVT applies; c = -16sqrt(3) / 3

    3. MVT applies; c = 8

    4. MVT applies; c = 16sqrt(3) / 3

    5. MVT does not apply

  3. Find the average value of f(x) = 2x3 + 3 on [3, 7]

    1. 689

    2. 158

    3. -158

    4. 4

    5. none of the above

Review
Lesson
      • Checkpoints (page 186)
        • L - #6
        • M - #20
        • N - #44
        • O - #48
    Exit Ticket
    • Posted on the board at the end of the class.
    Lesson Objective(s)
    • How can the first derivative be used to find relative extrema?
    • How can the first derivative be used to find intervals in which a function is increasing or decreasing?
    Standard(s)
    • APC.8

      • Apply the derivative to solve problems.

        • Includes:

          • ​analysis of curves and the ideas of concavity and monotonicity

          • optimization involving global and local extrema;

          • modeling of rates of change and related rates;

          • use of implicit differentiation to find the derivative of an inverse function;

          • interpretation of the derivative as a rate of change in applied contexts, including velocity, speed, and acceleration; and

          • differentiation of nonlogarithmic functions, using the technique of logarithmic differentiation.*

    Mathematical Practice(s)
    • #1 - Make sense of problems and persevere in solving them
    • #2 - Reason abstractly and quantitatively
    • #5 - Use appropriate tools strategically
    • #6 - Attend to precision
    • #8 - Look for and express regularity in repeated reasoning
    Past Checkpoints
    • Extrema (page 169)
      • A - #4
      • B - #6
      • C - #18
      • D - #22
      • E - #34
    • Rolle's Theorem (page 176)
      • F - #4
      • G - #10
      • H - #26
    • Mean Value Theorem (page 176-177)
      • I - #34
      • J - #42
      • K - #44