Review  Precalculus
 Extrema
 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)
Lesson
Exit Ticket
 Posted on the board at the end of the block.
Homework

Standard(s)
 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; andgeometric interpretation of differential equations via slope fields and the relationship between slope fields and the solution curves for the differential equations.
