Day 47 - Unit 3 Test - 03.11.16


    • Pre-calculus
      • Extrema
        • Minima
        • Maxima
      • Absolute and Relative Extrema (video)
      • Interval Notation
    • Extrema (video)/Critical Numbers (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?
      • How does Extreme Value Theorem work?
    • Increasing/Decreasing Functions (video) (checkpoints)
      • How can derivatives be used to find intervals of increasing and decreasing?
      • How can derivatives be used to find relative extrema?
    • Rolle's Theorem (video)/Mean Value Theorem (video) (Desmos Demonstration) (checkpoints)
    • Concavity and Inflection Points (video) (checkpoints)
      • How are derivative related to intervals of concave upwards and downwards?
    • Optimization

          • Unit 3 Test

          Exit Ticket
          • Posted on the board at the end of the block.

          • Study!

          • 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.