### Day 47 - Unit 3 Overview - 10.22.15

 Update Unit 3 Test this Friday! Bell RingerN/A Review Pre-calculusExtremaMinimaMaximaAbsoluteRelativeInterval NotationExtrema (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 (checkpoints)How are Rolle's Theorem and Mean Value Theorem related to differentiation?Rolle's Theorem (video)Mean Value Theorem (video) (demo video)Concavity and Inflection Points (checkpoints)How are derivative related to intervals of concave upwards and downwards?Optimization (checkpoints) (applications)How can differentiation be used to find optimal conditions? Lesson Exit Ticket N/AHomeworkN/A Help Request List Standard(s) APC.7Analyze 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 versaanalyzing 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.8Apply the derivative to solve problems.Includes:​analysis of curves and the ideas of concavity and monotonicityoptimization 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; anddifferentiation 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.