Day 46 - Unit 3 Overview - 10.21.15

  • Unit 3 Test this Friday!

Bell Ringer
    • N/A

    • Pre-calculus
      • Extrema
        • Minima
        • Maxima
        • Absolute
        • Relative
      • Interval Notation
    • Extrema (video) (checkpoints)
      • How can extrema be defined for a function?
      • How can critical numbers be calculated using derivatives?
      • How are critical numbers related to extrema?
      • Absolute and Relative Extrema (video)
      • Critical Numbers (video)
    • Increasing/Decreasing Functions (video) (checkpoints)
      • How are derivatives related to functions increasing and decreasing?
    • Rolle's Theorem & Mean Value Theorem (checkpoints)
      • How are Rolle's Theorem and Mean Value Theorem related to differentiation?
      • Rolle's Theorem (video)
      • Mean Value Theorem (video) (demo video)
    • Concavity and Inflection Points (checkpoints)
      • How are derivative related to intervals of concave upwards and downwards?
    • Optimization (checkpoints) (applications)
      • How can differentiation be used to find optimal conditions?

      Exit Ticket
      • N/A

      • N/A

      • 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
            • analyzing the geometric consequences of the Mean Value Theorem;
            • defining the relationship between the concavity of f and the sign of f"; and ​identifying points of inflection as places where concavity changes and finding points of inflection.
      • 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.*
              • *AP Calculus BC will also apply the derivative to solve problems.
                • Includes:
                  • ​analysis of planar curves given in parametric form, polar form, and vector form, including velocity and acceleration vectors;
                  • ​numerical solution of differential equations, using Euler’s method;
                  • ​l’Hopital’s Rule to test the convergence of improper integrals and series; and
                  • ​geometric interpretation of differential equations via slope fields and the relationship between slope fields and the solution curves for the differential equations.