What are critical numbers? numbers needed to solve problems values of x that cause a derivative to be equal to zero values of y that cause a derivative to be equal to zero values of x that cause a derivative to be undefined both b and d
How are relative extrema related to critical numbers? There is no relationship between critical numbers and relative extrema. Every relative extrema occurs at a critical number. Every critical number has a relative extrema. Critical numbers are only found at relative extrema. none of the above
Find the critical number(s) of the following: x = 1 x = 1 x = 0 undefined none of the above
Find the relative extrema for the following function: (1, 6) (1, 4) (0, 5) no relative extrema none of the above
Find and describe all extrema for the following function: on the interval Absolute max: (1, 4)  Absolute min: (2, 13)  No relative extrema Absolute min: (1, 4)  Absolute max: (2, 13)  Relative min: (0, 5) Absolute min: (1, 4)  Absolute max: (2, 13)  No relative extrema No extrema  none of the above
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?
Lesson  Challenge 3.2
 Using only calculus, how can we find extrema?
 Sketch a function with extrema.
 See me for hints.
 Increasing/Decreasing Functions (video)
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.
