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. 28--Quiz--Related Rates; Turvy due; Read section 3.1, Do p. 169 # 3-8, 13-16, 19-35 odds Nov. 30--p. 176-177 #11-23 odds, 39-46 Week of Dec. 3 Dec. 3--p. 186 #17-29 odds (TRP Lab Writeup due) Dec. 4--Function analysis sheet Dec. 5--Test 3; complete sheet on derivatives of e, ln and exponentials. Dec. 6--Read Section 3.4, Do p. 195 # 11-19 odds, 27-39 odds; watch video on the first derivative test http://www.brightstorm.com/math/calculus/applications-of-the-derivative/the-first-derivative-test-for-relative-maximum-and-minimum/ Dec. 7-- HW--AP Function Analysis Packet Week of Dec. 10 Dec. 10--Multiple Choice Monday #2; p. 215 # 7, 8, 10, 15-18 Dec. 11--Practice with functions and curve sketching; HW--Curve sketching packet Dec. 12--HW--Behavior of Functions sheet Dec. 13--Mini quiz--AP Function Analysis Dec. 14--Optimization--Read pp. 218-222, do pp. 223-225 #19, 20, 22, 25, 27, 33 Week of Dec. 17 Dec. 17--Review Book--pp 125-126 # 1-6 Dec. 18--Optimization Problems Dec. 19--Optimization Problems Dec. 20--Optimization quiz; Optimization Problems Dec. 21--HW--Holiday Practice Bonus An open-top 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 |
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