Day 37 - Extrema - 10.08.14

Updates
  • Summative Exam 1 on Friday!
  • New Remediation Rules
    • If you don't make a request, you won't be allowed to remediate or reassess.
    • Use your notes to make test corrections
    • Complete similar problems to the problems you lost points on
    • Write what you did wrong on each problem

Bell Ringer (due by the end of the day!)


    Extrema

  1. Find the value of the derivative (if it exists) of the function f(x) = 15 - |x| at point (0, 15).

    1. 0

    2. does not exist

    3. -15

    4. 15

    5. none of the above

  2. Find all of the critical numbers for f(x) = (9 - x2). Note: f(x) = (9 - x^2)^(3/5)

    1. -3, 0, 3

    2. 3

    3. 3, -3

    4. 0

    5. none of the above

  3. Find the derivative of the function f(x) = x2 / (x2 + 64) at point (0, 0).

    1. 0

    2. 1

    3. -1

    4. 1/9

    5. -1/9

  4. Locate the absolute extrema of the function f(x) = 2x2 + 12x - 4 on the closed interval [-6, 6].

    1. no absolute max; absolute min: f(6) = 140

    2. absolute max: f(-3) = -22; absolute min: f(6) = 140

    3. absolute max: f(6) = 140; no absolute min

    4. absolute max: f(6) = 140; absolute min: f(-3) = -22

    5. no absolute max or min



Review
  • Prerequisites
    • Interval Notation
    • Maxima/Minima
    • Zero Product Property
    • Finding Minima/Maxima Graphically

Lesson
    • Checkpoints
      • A - page 169 #4
      • B - page 169 #6
      • C - page 169 #18
      • D - page 169 #22
      • E - page 169 #34
  • Summative Exam 1 Questions
    • page 91 #5-24 (odds), 27-30 (odds)
    • page 92 #35-39 (odds), 45, 49, 53, 57, 59, 67
    • page 158 #1, 9, 21, 27, 39, 43, 45, 69-75 (odds), 83, 93, 103, 115

Exit Ticket
  • N/A
Lesson Objective(s)
  • How can derivatives be used to find extreme values of a function?

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