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Calculus For Business

by: Mozell Veum

Calculus For Business MAC 2233

Mozell Veum
GPA 3.56


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This 2 page Study Guide was uploaded by Mozell Veum on Monday October 12, 2015. The Study Guide belongs to MAC 2233 at Florida International University taught by Staff in Fall. Since its upload, it has received 74 views. For similar materials see /class/221713/mac-2233-florida-international-university in Calculus and Pre Calculus at Florida International University.

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Date Created: 10/12/15
MAC 2233 TEST TWO STUDY GUIDE Test Two will cover sections 35 41 42 and 43 As with Test One the exam will consist of two parts one requiring a graphing calculator and the other forbidding the calculator The noncalculator portion of the test will consist of several problems involving nding rst and second derivatives by hand using our required memorized differentiation formulas and the Product Rule There will be at least one problem LBCe C LBC Th 1Be cquot 1 Becki or Cat 1 Ber239 e e I 6 II e I calculator part of the exam will consist entirely ofa mix of homework problems and problems very similar to those of the homework The homework for sections 35 41 42 and 43 the test sections that is can be found at httpwww uedustorferr2233HWhtml Below is a section be section summary requiring the Logistic Function Differentiation Formula SECTION 35The Product Rule Be able to use the Product Rule to solve typical problems requiring the use of the derivative Do not overlook problems such as 35 and 7 on page 212 SECTION 41 Approximatng Change Know the formulas on the bottom of page 230 and how to use them to solve reallife problems Also be able to both compute marginal cost revenue and profit and use them along with the page 230 formulas to solve problems SECTION 42Relative and Absolute Extrema KEY FACTS o lffis a continuous function on a closed interval ab then fwill have an absolute minimum and absolute maximum on 0 Relative Extrema peaksquot and valleys can occur on the interiors of closed intervals but not an endpoint Endpoints can be absolute extrema but not relative extrema peaksquot and valleysquot Relative extrema can be absolute extrema also 0 lfa function fhas a relative extrema on any interval then it will occur at points where either f is zero or f does not exist This is equivalent to saying that ifthere are no points on for which f is zero or f does not exist then fhas no relative extrema on lnstead fwill be increasing or decreasing monotonic on Therefore to nd possible points where fhas relative extrema solve the equation f x0 and also nd any points xfor which f does not exist Those points x are called critical points Please keep in that mind that relative extrema occur if and only if the derivative f changes sign at x o If f is always positive valued on an interval then fis increasing on If f is always negative valued on an interval then fis decreasing on Know how to use the above key facts to solve applications problems Typical testtype applications problems are the section 42 hw problems SECTION 43INFLECTION POINTS lnflections points are those which a function fchanges concavity ln applications inflection points are the points of most rapid increase or decrease and least rapid increase or decrease See figure 415 on page 256 ln ection points can occur only where the second derivative fquot is zero and has a sign change Please do not confuse points of least or most rapid increase or decrease with relative maximums and relative minimum The former points require using the second derivative while the latter points need the first Also be aware a function with a second derivative f that is positive valued on I is concave up on I and a function with a second derivative f that is negative valued on I is concave down on I Geometrically concave up means the graph lies above its tangent lines and concave down is lying below its tangent lines Drawing the always concave up graph y x2 and the always concave down graph y x2 can help understand the tangent line relationships to concavity


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