Derivatives have several applications. Related rates problems involve changes in one parameter that affect another. We can examine derivatives to find out about the original function. For example, if the first derivative (slope) is positive, then the function is increasing on that interval. When the first derivative changes from positive to negative, we will find that the function goes from increasing to decreasing, which means a maximum is located there. If the second derivative is positive (rate of change of the slope), then the function is concave up. When the second derivative changes sign, we will find a point of inflection. We can also use derivatives in problems of optimization allowing us to find the maximum profit, the minimum time, the maximum volume, the minimum cost, etc.
Notes and Handouts 
AssignmentsWeek of Nov. 26
Nov. 28QuizRelated Rates; Turvy due; Read section 3.1, Do p. 169 # 38, 1316, 1935 odds Nov. 30p. 176177 #1123 odds, 3946 Week of Dec. 3 Dec. 3p. 186 #1729 odds (TRP Lab Writeup due) Dec. 4Function analysis sheet Dec. 5Test 3; complete sheet on derivatives of e, ln and exponentials. Dec. 6Read Section 3.4, Do p. 195 # 1119 odds, 2739 odds; watch video on the first derivative test http://www.brightstorm.com/math/calculus/applicationsofthederivative/thefirstderivativetestforrelativemaximumandminimum/ Dec. 7 HWAP Function Analysis Packet Week of Dec. 10 Dec. 10Multiple Choice Monday #2; p. 215 # 7, 8, 10, 1518 Dec. 11Practice with functions and curve sketching; HWCurve sketching packet Dec. 12HWBehavior of Functions sheet Dec. 13Mini quizAP Function Analysis Dec. 14OptimizationRead pp. 218222, do pp. 223225 #19, 20, 22, 25, 27, 33 Week of Dec. 17 Dec. 17Review Bookpp 125126 # 16 Dec. 18Optimization Problems Dec. 19Optimization Problems Dec. 20Optimization quiz; Optimization Problems Dec. 21HWHoliday Practice Bonus An opentop cylindrical tank with a volume of ten cubic feet is to be made from a sheet of steel. Find the dimensions of the tank that will require as little material used in the tank as possible. Submit answers to Dr. Vincent or Mrs. Bratt by Friday, Jan. 4, 2013 
AP Calculus 
