### Day 35 - Extrema - 10.06.14

 UpdatesSummative Exam 1 on Friday!Bell RingerExtremaWhich of the following matches the interval notation of [-1, 3]?-1 < x < 3-1 > x > 3-1 ≤ x ≤ 3-1 ≥ x ≥ 3none of the aboveSolve the following: 6x3 - 6x2 = 00-11both a and cnone of the aboveFind the maxima or minima of the following: x2 - 4x + 5 on the interval [-1, 3](2, -1)(2, 1)(0, 1)(2, 0)none of the aboveFind any local (relative) maxima or minima of the following: 2x3 - 9x2 + 12x - 2 on the interval [-1, 3](1, 3)(2, -2)(2, 2)both a and cnone of the aboveFind the maxima or minima of the following: f(x) = |x + 3|(3, 0)(0, 3)(-3, 0)(0, 3)none of the aboveReviewPrerequisitesInterval NotationMaxima/MinimaZero Product PropertyFinding Minima/Maxima GraphicallyLessonExtremaDefinitionExtreme 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 QuestionsExit TicketPosted on the board at the end of the block. Lesson Objective(s)How can derivatives be used to find the minimum and maximum 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