Bell RingerFind all of the critical numbers for . –3, 0, 3 3 3, –3 0 none of the above
Locate the absolute extrema of the function on the closed interval [–6, 6] No absolute max, Absolute min: Absolute max: , Absolute min: Absolute max: , No absolute min Absolute max: , Absolute min: No absolute max or min
Determine whether Rolle's Theorem can be applied to the function on the closed interval [–1, 5]. If Rolle´s Theorem can be applied, find all values of c in the open interval (–1, 5) such that . Rolle’s Theorem applies; c = –2 Rolle’s Theorem applies; c = 0.5 Rolle’s Theorem does not apply Rolle’s Theorem applies; c = 2 both a and d
Determine whether the Mean Value Theorem can be applied to the function on the closed interval [0, 16]. If the Mean Value Theorem can be applied, find all numbers c in the open interval (0, 16) such that . MVT applies; c = 4 MVT applies; c = MVT applies; c = 8 MVT applies; c = MVT does not apply
Find all intervals on which is concave upward.
 none of these
 Precalculus
 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
 How are Rolle's Theorem and Mean Value Theorem related to differentiation?
 Concavity and Inflection Points
 How are derivative related to intervals of concave upwards and downwards?
Lesson
 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.
