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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 Jennifer Taggart in Fall. Since its upload, it has received 32 views. For similar materials see /class/192079/math-112-university-of-washington in Mathematics (M) at University of Washington.

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Date Created: 09/09/15

MATH 112 REVIEW FOR EXAM II OPTIMIZATION I Derivative Rules 0 There will be a page of derivatives on the exam Know how to apply all the derivative rules WS 12 and 13 II Functions of One Variable 0 Be able to distinguish between local and global optima 0 Be able to nd the global maximum and minimum of a function y fz on the interval from x a to z b7 using the fact that optima may only occur where fz has a horizontal tangent line and at the endpoints of the interval Step 1 Compute f z Step 2 Find all values of x at which f z 0 Step 3 Plug all the values of z from Step 2 that are m the intervalfmm a to b and the endpoints of the interval into the function Step 4 Sketch a rough graph of fz and pick off the global max and min Be familiar with the following two applications Maximizing TRq starting with a demand curve WS 15 7 Optimizing the slope of a diagonal line through a given curve WS 16 Understand how to use the Second Derivative Test WS 17 If f a 0 and f a gt 07 then fz has a local min at z a f a lt 07 then fz has a local max at z a f a 07 then the test tells you nothing IMPORTANT For the Second Derivative Test to work7 you must have f a 0 If f a gt 0 but f a 31 07 then the graph of fz is concave up at z a but fz does not have a local min there III Functions of Two Variables 0 Be able to compute overall7 incremental7 and instantaneous rates of change of a function of two variables WS 18A 0 Be able to compute partial derivatives using all the derivative rules 0 Know how to nd the candidates for maxima and minima in a function of two variables Take both partial derivatives7 set them equal to 07 and solve the resulting system of equations 0 Know the procedure for nding the best tting line for a set of data WS 18 Step 1 Given n points ml7 compute Em Eyi Ezlz Egg Exiyi Step 2 Use the sums from Step 1 to nd the formula for the mean squared error function Ebm Step 3 Compute and Step 4 Solve the system of equations 0 and 0 for m and b These are the slope and y intercept of the best tting line y ms b 0 Know when its appropriate to take logs to make exponential data look linear WS 14 Be able to convert a linear model for lny into an exponential model for y Be able to solve a linear programming problem WS 19 Step 1 Find the objective function Step 2 Find the constraints Step 3 Graph the feasible region and nd its vertices Step 4 Plug all vertices into the objective function The max and min of the objective function must occur at one of the vertices

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