Critical Numbers
Extrema
Increasing/Decreasing Functions
Relative Extrema
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?
Lesson  Challenge 3.3
 Rolle's Theorem
 Sketch a graph of a function on a closed interval [a, b] that:
 has endpoints with equal yvalues.
 Sketch a graph of a function on a closed interval [a, b] that:
 has endpoints with equal yvalues
 has no point that has a slope of zero
 Sketch a graph of a function on a closed interval [a, b] that:
 has endpoints with equal yvalues
 has no point that has a slope of zero
 is continuous
 Sketch a graph of a function on a closed interval [a, b] that:
 has endpoints with equal yvalues
 has no point that has a slope of zero
 is continuous from [a, b]
 is differentiable on the interval (a, b)
 Mean Value Theorem
 Sketch a graph of a function on a closed interval [a, b] that:
 has endpoints with unequal yvalues.
 Sketch a graph of a function on a closed interval [a, b] that:
 has endpoints with unequal yvalues
 has no points with equal to the slope of points a and b
 Sketch a graph of a function on a closed interval [a, b] that:
 has endpoints with unequal yvalues
 has no points with equal to the slope of points a and b
 is continuous
 Sketch a graph of a function on a closed interval [a, b] that:
 has endpoints with unequal yvalues
 has no points with equal to the slope of points a and b
 is continuous from [a, b]
 is differentiable on the interval (a, b)
 Videos
 Practice
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.
