Day 45 - Optimization - 03.17.15

  • 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!


Bell Ringer
  • Posted on the board!

  • 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.
  • Concavity and Inflection Points
    • 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.
    1. Limits at Infinity
      • How can limits be used to find horizontal asymptotes of the graph of a function? (video)
          1. Determine horizontal asymptotes using limits.
          2. Determine finite limits at infinity.
          3. Determine infinite limits at infinity.


      Exit Ticket
      • Posted on the board at the end of the block
      Lesson Objective(s)
      • How can differentiation be used to find optimal conditions of a scenario?
        1. Determine the conditions that optimize a situation.

              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