### Day 44 - Limits at Infinity - 10.20.14

 UpdatesHand back Quiz 7Go over Quiz 7Average = 78%Bell RingerConcavity and Inflection PointsFind all intervals on which f(x) = (x + 1) / (x - 3) is concave upward.(1. ∞)(-∞, ∞)(-∞, 3)(3, ∞)none of the aboveFind all points of inflection: f(x) = x4 / 12 - 2x2 + 15(2, 0)(2, 0); (-2, 0)(0, 15)(2, 25/3); (-2, 25/3)none of theseWhat is the horizontal asymptote for the following: f(x) = 4 - 6 / x3?y = -4y = 0x = 4y = 4none of the aboveWhat is the horizontal asymptote for the following: f(x) = (3x - 2) / (6x - 1)y = ½y = -½x = ½y = 3none of the aboveReviewPrerequisitesInterval NotationMaxima/MinimaZero Product PropertyFinding Minima/Maxima GraphicallyExtremaRolle's TheoremMean Value TheoremIncreasing and Decreasing FunctionsFirst Derivative TestConcavity and Inflection PointsSecond Derivative TestLessonLimits at InfinityCheckpointsExit TicketPosted at the end of the block. Lesson Objective(s)How can limits at infinity be calculated?How are limits at infinity related to horizontal asymptotes?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 - #52