Last Name:First Name:Math La Bxam #2: Tuesday, November 23,1999sEcrroN (CIRCLE oNE):Bing Cheng Bing Cheng Robert Winters Laura DeMarcoMWF l0 MWF I I IvtWF l0 MWF 12Manoj Viswanathan (CA) Eiichi Miyasaka (CA) Sahir Islam (CA) Brian Shaffer (CA)Lisa CarboneTTh IOKaren Acquista (CA)Rodolfo Perez (CA)Lisa CarboneTTh I l:30Peter Hamel (CA)Grisha MihalkinTTh I 1:30Jacob Honoroff(CA)QuestionPointsScoreI l52 t4Jl64t45 t46 l57t2Total100The time allotted for this exam is 90 minutes.Calculators are not permitted.Justify your answers carefully. No partial credit can be given for unsubstantiated answers.(1) Consider the two small Zairian towns of Abedi and Bueya, which currently cannot be reached by road'The main road from Kinshasa to Matadi passes 10 km south of the two towns'The government plans to build a road system connecting the two towns to the main road , as shown in thediagiam. How fai from the main road sirould the junction point be chosen to minimize the total length ofthe new roads?AbediBueyajunctionI10 kmIImain road- JOkm- - -(2) A creature moves along the x-axis in such a way that its acceleration is given by a(t):4 - l2t.We also know that when t: I it is at the position x: 3 and has zero velocity at that moment.Where will the creature be when t:2?(3) A function /(x) and its first and second derivatives are given belowx-la) Identify any .r ory intercepts for the graph of thisfunction.b) Find any critical points and determine whether they arerelative maxima or minima or neither.c) Find any points of inflection.d) Find any vertical asymptotes for this graph.e) Find any horizontal asymptotes for this graph.f) Give a rough sketch of the graph of this function,illustrating all of the features you found in parts a)through e)..f (x) =.f '(x) =x'-2x-x'+2x-21x2 -2x)22(x -l)(x' *2x + 4)(x'-2x)'.f "(x) =(4) A manufacturing plant has a capacity of 25 articles per week. Experience has shown that n articles can besoldatapriceofpdollarseachwherep=ll0-2nandthecostofproducingnarticlesisknowntobe600 + 20n + n' dolla.s. How many articles should be made each week to give the largest profit?(5) A man 6 feet tall walks away from a source of light 20 feet above the ground at a speed of 3 feet persecond. At what rate is the shadow of his head moving along the ground?(6) Findcosx - I(a) lrm 1r+r., X_(b) lim ::-' ' t-** 3Xt +l(c) lim{flI' ' r-+l X'-1(7) Find the point on the parabola y: x2 that is closest to the point (4,
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