Day 41 - Concavity and Inflection Points - 03.11.15

  • Unit 3 Test on 3/27!
    • If you are leaving for spring break early, please make arrangements with me to take the test before break!
  • Last Week to Retake Unit 2 Test
    • Parent-Teacher Conferences will be on Friday!
    • Questions on previous Checkpoints?


    Bell Ringer
    1. First Derivative Test

    1. First Derivative Test

    1. Points of Inflection

    1. Concavity

    • Extrema/Critical Numbers (video)
      • How is the derivative used to locate the minimum and maximum values of a function on a closed interval?
        • Find critical numbers using differentiation.
        • Find extrema on a closed interval using differentiation.
    • Rolle's Theorem (videoand Mean Value Theorem  (video)
      • How are Rolle's Theorem and Mean Value Theorem related to differentiation?
        • Apply understanding of Rolle’s Theorem and the Mean Value Theorem.
    • Increasing/Decreasing Functions (video)
      • How can the first derivative to determine whether a function is increasing or decreasing?
        1. Determine intervals on which a function is increasing or decreasing.
        2. Apply the First Derivative Test to find relative extrema of a function.


    Exit Ticket
    • Posted on the board at the end of the block
    Lesson Objective(s)
    • How can the second derivative be used to determine the concavity of intervals of a function? (video)
      1. Determine intervals on which a function in concave upward or downward.
      2. Apply the Second Derivative Test to find inflection points of a function.

            In-Class Help Requests

            • APC.4
              • Investigate asymptotic and unbounded behavior in functions.
                • Includes:
                  • describing and understanding asymptotes in terms of graphical behavior and limits involving infinity
            • 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

            Past Checkpoints