Day 37 - Rolle's Theorem and Mean Value Theorem - 10.07.15

  • Summative Exam 1
    • Average = 75%

Bell Ringer

  1. Critical Numbers

  1. Extrema

  1. Increasing/Decreasing Functions

  1. Relative Extrema

  • 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?


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


In-Class Help Requests

  • 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.