Day 36 - Extrema/Critical Numbers - 03.04.15

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Questions
Bell Ringer

  1. Find the x-coordinate that has a horizontal tangent line for the following:

    1. -2

    2. 0

    3. 2

    4. 3

    5. none of the above

  2. Does the point in #1 occur at a maximum or a minimum on the graph?

    1. maximum

    2. minimum

    3. neither

  3. Find the x-coordinate in which the following function does not have a derivative:

    1. 0

    2. 2

    3. -2

    4. 1

    5. none of the above

  4. Does the point in #3 occur at a maximum or a minimum on the graph?

    1. maximum

    2. minimum

    3. neither
Review
  • N/A
Lesson
Exit Ticket
  • N/A
Lesson Objective(s)
  • How is the derivative used to locate the minimum and maximum values of a function on a closed interval?
Skills
    1. Find critical numbers using differentiation.
    2. Find extrema on a closed interval using differentiation.

      In-Class Help Requests

      Standard(s)
      • APC.5
        • Investigate derivatives presented in graphic, numerical, and analytic contexts and the relationship between continuity and differentiability.
          • The derivative will be defined as the limit of the difference quotient and interpreted as an instantaneous rate of change.
      • APC.6
        • ​The student will investigate the derivative at a point on a curve.
          • Includes:
            • finding the slope of a curve at a point, including points at which the tangent is vertical and points at which there are no tangents
            • using local linear approximation to find the slope of a tangent line to a curve at the point
            • ​defining instantaneous rate of change as the limit of average rate of change
            • approximating rate of change from graphs and tables of values.
      • APC.7
        • Analyze the derivative of a function as a function in itself.
          • Includes:
            • comparing corresponding characteristics of the graphs of f, f', and f''
            • ​defining the relationship between the increasing and decreasing behavior of f and the sign of f'
            • ​translating verbal descriptions into equations involving derivatives and vice versa
            • defining the relationship between the concavity of f and the sign of f "
      • APC.9
        • Apply formulas to find derivatives.
          • Includes:
            • derivatives of algebraic and trigonometric functions
            • derivations of sums, products, quotients, inverses, and composites (chain rule) of elementary functions
            • derivatives of implicitly defined functions
            • higher order derivatives of algebraic and trigonometric functions
      Past Checkpoints
      • N/A