### Day 45 - Optimization - 10.21.14

 UpdatesUnit 3 Test next Friday, 10/31!Bell RingerLimits at InfinityFind the limit of 01does not exist¼7/4Find the limit of ∞-1-∞51Find the limit of ∞-∞05/46Find the limit of ∞7801Which of the following has a horizontal asymptote at y = -½none of theseReviewPrerequisitesInterval NotationMaxima/MinimaZero Product PropertyFinding Minima/Maxima GraphicallyExtremaRolle's TheoremMean Value TheoremIncreasing and Decreasing FunctionsFirst Derivative TestConcavity and Inflection PointsSecond Derivative TestLimits at InfinityHorizontal AsymptotesLessonOptimizationFind two positive numbers that have a product of 100 and the sum is a minimum.Find the length and width of a rectangle that has a perimeter of 100 feet and a maximum area.CheckpointsExit TicketPosted at the end of the block. Lesson Objective(s)How can derivatives be used to find optimum conditions?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#5 - Use appropriate tools strategically#6 - Attend to precision#8 - Look for and express regularity in repeated reasoningPast CheckpointsExtrema (page 169)A - #4B - #6C - #18D - #22E - #34Rolle's Theorem (page 176)F - #4G - #10H - #26Mean Value Theorem (page 176-177)I - #34J - #42K - #44Increasing/Decreasing Functions (page 186)L - #6M - #20N - #44O - #48Concavity and Points of Inflection (page 195)P - #6Q - #16R - #18S - #20T - #24U - #32V - #38W - #52Limits at InfinityCheckpoints