Day 45 - Optimization - 10.21.14

Updates
  • Unit 3 Test next Friday, 10/31!
Bell Ringer
  • Limits at Infinity

  1. Find the limit of

    1. 0

    2. 1

    3. does not exist

    4. ¼

    5. 7/4

  2. Find the limit of 

    1. ∞

    2. -1

    3. -∞

    4. 5

    5. 1

  3. Find the limit of

    1. ∞

    2. -∞

    3. 0

    4. 5/4

    5. 6

  4. Find the limit of

    1. ∞

    2. 7

    3. 8

    4. 0

    5. 1

  5. Which of the following has a horizontal asymptote at y = -½

    5. none of these
Review
Lesson
  • Optimization
    • Find two positive numbers that have a product of 100 and the sum is a minimum.
    • Find the length and width of a rectangle that has a perimeter of 100 feet and a maximum area.
Exit Ticket
  • Posted at the end of the block.
Lesson Objective(s)
  • How can derivatives be used to find optimum conditions?
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
  • Increasing/Decreasing Functions (page 186)
    • L - #6
    • M - #20
    • N - #44
    • O - #48
  • Concavity and Points of Inflection (page 195)
    • P - #6
    • Q - #16
    • R - #18
    • S - #20
    • T - #24
    • U - #32
    • V - #38
    • W - #52
  • Limits at Infinity