Day 40 - Rolle's Theorem and Mean Value Theorem - 10.14.14

Updates
Bell Ringer


  • Extrema

  1. Find the critical values for the following function: f(x) = sin(x) + cos(x) on the interval [0, 2π].

    1. π / 4

    2. 5π / 4

    3. π / 4, 5π / 4

    4. 7π / 4

    5. none of the above

  2. Find all the relative extrema for the following function: f(x) = sin(x) + cos(x) on the interval [0, 2π].

    1. Relative Max: (5π / 4, sqrt(2)); Relative Min: (π / 4, -sqrt(2))

    2. Relative Max: (π / 4, sqrt(2)); Relative Min: (-π / 4, -sqrt(2))

    3. Relative Max: (π / 4, sqrt(2)); Relative Min: (5π / 4, -sqrt(2))

    4. Relative Max: (π / 4, sqrt(2)); Relative Min: (5π / 4, sqrt(2))

    5. none of the above
Review
Lesson
    • Rolle's Theorem (pronounced "rawls")
      • Connecting Two Points without an Extrema Activity
      • Walking in a Circle Activity
      • Mean Value Theorem Checkpoints (page 176-177)
        • I - #34
        • J - #42
        • K - #44
    Exit Ticket
    • Posted on the board at the end of the class.
    Lesson Objective(s)
    • How can Rolle's Theorem be used and applied to solve problems?
    • How can Mean Value Theorem be used and applied to solve problems?
    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
    • #3 - Construct viable arguments and critique the reasoning of others
    • #5 - Use appropriate tools strategically
    • #6 - Attend to precision
    • #7 - Look for and make use of structure
    • #8 - Look for and express regularity in repeated reasoning
    Past Checkpoints
    • Extrema (page 169)
      • A - #4
      • B - #6
      • C - #18
      • D - #22
      • E - #34