### Day 40 - Rolle's Theorem and Mean Value Theorem - 10.14.14

 UpdatesGo over previous Bell RingerBreakdownAverage = 76%Bell RingerExtremaFind the critical values for the following function: f(x) = sin(x) + cos(x) on the interval [0, 2π].π / 45π / 4π / 4, 5π / 47π / 4none of the aboveFind all the relative extrema for the following function: f(x) = sin(x) + cos(x) on the interval [0, 2π].Relative Max: (5π / 4, sqrt(2)); Relative Min: (π / 4, -sqrt(2))Relative Max: (π / 4, sqrt(2)); Relative Min: (-π / 4, -sqrt(2))Relative Max: (π / 4, sqrt(2)); Relative Min: (5π / 4, -sqrt(2))Relative Max: (π / 4, sqrt(2)); Relative Min: (5π / 4, sqrt(2))none of the aboveReviewPrerequisitesInterval NotationMaxima/MinimaZero Product PropertyFinding Minima/Maxima GraphicallyExtremaLessonRolle's Theorem (pronounced "rawls")Connecting Two Points without an Extrema ActivityWalking in a Circle ActivityRolle's Theorem Checkpoints (page 176)G - #10H - #26Mean Value TheoremMean Value Theorem Checkpoints (page 176-177)I - #34J - #42K - #44Exit TicketPosted on the board at the end of the class. Lesson Objective(s)How can Rolle's Theorem be used and applied to solve problems?How can Mean Value Theorem be used and applied to solve problems?Standard(s)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.*Mathematical Practice(s)#1 - Make sense of problems and persevere in solving them#2 - Reason abstractly and quantitatively#3 - Construct viable arguments and critique the reasoning of others#5 - Use appropriate tools strategically#6 - Attend to precision#7 - Look for and make use of structure#8 - Look for and express regularity in repeated reasoningPast CheckpointsExtrema (page 169)A - #4B - #6C - #18D - #22E - #34