Day 35 - Extrema - 10.06.14

Updates
  • Summative Exam 1 on Friday!

Bell Ringer


Extrema

  1. Which of the following matches the interval notation of [-1, 3]?

    1. -1 < x < 3

    2. -1 > x > 3

    3. -1 ≤ x ≤ 3

    4. -1 ≥ x ≥ 3

    5. none of the above

  2. Solve the following: 6x3 - 6x2 = 0

    1. 0

    2. -1

    3. 1

    4. both a and c

    5. none of the above

  3. Find the maxima or minima of the following: x2 - 4x + 5 on the interval [-1, 3]

    1. (2, -1)

    2. (2, 1)

    3. (0, 1)

    4. (2, 0)

    5. none of the above

  4. Find any local (relative) maxima or minima of the following: 2x3 - 9x2 + 12x - 2 on the interval [-1, 3]

    1. (1, 3)

    2. (2, -2)

    3. (2, 2)

    4. both a and c

    5. none of the above

  5. Find the maxima or minima of the following: f(x) = |x + 3|

    1. (3, 0)

    2. (0, 3)

    3. (-3, 0)

    4. (0, 3)

    5. none of the above

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 the minimum and maximum 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