### Day 37 - Extrema - 10.08.14

 UpdatesSummative Exam 1 on Friday!New Remediation RulesIf you don't make a request, you won't be allowed to remediate or reassess.Use your notes to make test correctionsComplete similar problems to the problems you lost points onWrite what you did wrong on each problemBell Ringer (due by the end of the day!)    ExtremaFind the value of the derivative (if it exists) of the function f(x) = 15 - |x| at point (0, 15).0does not exist-1515none of the aboveFind all of the critical numbers for f(x) = (9 - x2)⅗. Note: f(x) = (9 - x^2)^(3/5)-3, 0, 333, -30none of the aboveFind the derivative of the function f(x) = x2 / (x2 + 64) at point (0, 0).01-11/9-1/9Locate the absolute extrema of the function f(x) = 2x2 + 12x - 4 on the closed interval [-6, 6].no absolute max; absolute min: f(6) = 140absolute max: f(-3) = -22; absolute min: f(6) = 140absolute max: f(6) = 140; no absolute minabsolute max: f(6) = 140; absolute min: f(-3) = -22no absolute max or minReviewPrerequisitesInterval NotationMaxima/MinimaZero Product PropertyFinding Minima/Maxima GraphicallyLessonExtremaVideo LessonsDefinitionExtreme Value TheoremAbsolute vs. Relative ExtremaCritical NumbersTesting for Critical NumbersFinding ExtremaCheckpointsA - page 169 #4B - page 169 #6C - page 169 #18D - page 169 #22E - page 169 #34Summative Exam 1 Questionspage 91 #5-24 (odds), 27-30 (odds)page 92 #35-39 (odds), 45, 49, 53, 57, 59, 67page 158 #1, 9, 21, 27, 39, 43, 45, 69-75 (odds), 83, 93, 103, 115Exit TicketN/A Lesson Objective(s)How can derivatives be used to find extreme values of a function?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 reasoning