Day 36 - Extrema - 10.07.14

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


    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)⅗.

    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
  • Extrema
    • Definition
    • Extreme Value Theorem
    • Absolute vs. Relative Extrema
    • Critical Numbers
      • Testing for Critical Numbers
    • Finding Extrema
    • 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
Exit Ticket
  • Posted on the board at the end of the block.
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