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# BUSINESS &ECON CALC MATH 112

UW

GPA 3.76

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This 2 page Class Notes was uploaded by Addison Beer on Wednesday September 9, 2015. The Class Notes belongs to MATH 112 at University of Washington taught by Alexandra Nichifor in Fall. Since its upload, it has received 14 views. For similar materials see /class/192056/math-112-university-of-washington in Mathematics (M) at University of Washington.

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Date Created: 09/09/15

Math 112 Final Exam Review 1 Derivatives derivatives as the slope of a tangent line using secant lines to compute the derivative derivative as instantaneous rate of change However also remember average rates of change incremental eg average speed overall eg average trip speed derived graphs what does the derived graph off tell you about f derivative rules partial derivatives 2 Optimization using the derivative or not finding localglobal optima maxmin second derivative test concavity linear programming 3 Integration 1 I f xdx area of stuff above x axis area of stuff below x axis b counting squares and using trapezoids to approximate I f xdx b using FTC to compute I f xdx given a formula for x I f xdx the anti derivative of fx remember the C computing areas between curves using integrals 4 The Big Examples a DistanceSpeed speed derivative of distance 0 if given a graph of distance find instantaneous speed using slope of tangent line 0 if given a formula for distance take derivative to get instantaneous speed distance integral of speed 0 if given only a graph of speed find distance by taking signed areas 0 if given a formula for speed take anti derivatives to get distance caution what distance do you get b TRMRTCMC MRderivative of TR 0 given the graph of TR find MR using slope of tangent line 0 given the formula for TR find MR by taking the derivative TRintegral of MR 0 given the graph of MR find TR by taking areas 0 given the formula for MR find TR by antidifferentiating TCMC are similar except you must consider FC TC integral of MC FC 0 given graph of MC find TC by taking areas and adding on FC 0 given formula for MC find TC by antidifferentiating and adding on FC profit area between MR amp MC when MRgtMC area between MR amp MC when MRltMC FC

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