Day 46 - Optimization - 10.22.14

Updates
  • Unit 3 Test this Friday, 10/24!
Bell Ringer
  • Optimization

  • A farmer has 160 feet of fencing to enclose 2 adjacent rectangular pig pens. The farmer is looking to maximize the area of the pen.


  1. Which formula should be differentiated?

    1. Perimeter

    2. Area

    3. Surface Area

    4. Volume

    5. none of the above

  2. What overall dimensions should be used to maximize the enclosed area?

    1. 20 ft x 20 ft

    2. 53.3 ft x 20 ft

    3. 26.7 ft x 20 ft

    4. 53.3 ft x 40 ft

    5. none of the above

  3. What is the maximum area possible?

    1. 400 ft2

    2. 533.3 ft2

    3. 800 ft2

    4. 1066.7 ft2

    5. none of the above

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