MA 123 — Elementary CalculusSECOND MIDTERMSpring 200903/11/2009Name: Sec.:Do not remove this answer page — you will return the whole exam. You will be allowed two hoursto complete this test. No books or notes may be used. You may use a graphing calculator during theexam, but NO calculator with a Computer Algebra System (C AS) or a QWERTY keyboard is permitted.Absolutely no cell phone use during the exam is allowed.The exam consists of 15 multiple choice q uestions. Record your answers on this page by filling in thebox corre sponding to the correct an swer. For e xample, if (b) is correct, you must writeabcdeDo not circle answers on this page, but please do circle the letter of each correct response in the body ofthe exam. It is your responsibility to make it CLEAR which response has been chosen. You will not getcredit unless the correct answer has been marked on both this page and in the body of the exam.GOOD LUCK!1.abcde2.abcde3.abcde4.abcde5.abcde6.abcde7.abcde8.abcde9.abcde10.abcde11.abcde12.abcde13.abcde14.abcde15.abcdeFor grading use:number ofcorrect problems(out of 15)Total(out of 100 pts)1MA 123 — Elementary CalculusSECOND MIDTERMSpring 2 00903/11/2009Please make sure to list the correct section number on the front page of your exam.In case you forgot your section number, consult the following table:Section # Instructor Lectures001 A. Corso MWF 12:00 pm-12:50 pm, CB 106002 M. Shaw MWF 2 : 00 pm-2:5 0 pm, KAS 21 3003 T. Chapman TR 12:30 pm-1:45 pm, CB 118004 M. Shaw TR 9:30 am-10:4 5 am, FB 213005 M. Shaw TR 12:30 pm-1:4 5 pm, C B 217401 T. Muldoon TR 6:00 pm-7:15 pm, CB 339402 T. Muldoon TR 7:30 pm-8:45 pm, CB 3392Multiple Choice QuestionsShow all your work on the page where the question appears.Clearly mark your answer both on the cover page on this examand in the corresponding questions that follow.1. Suppose that f(x) =13(x2− 8)7. Find f′(3).Possibilities:(a) 7(b) 14(c) 28(d) 42(e) 562. Suppose that f(x) =3x − 42x + 5. Find f′(−1).Possibilities:(a) −23/9(b) 23/3(c) −23/3(d) 23/9(e) 3/233. Suppose that f(x) = ln(x2+ 2x + 4). Find f′(1).Possibilities:(a) 4/7(b) 5/7(c) 2/5(d) 3/5(e) 5/634. Suppose that h(x) = f(g(x)). Assume that f (4) = 5, f′(4) = 3, g(3) = 4, and g′(3) = 4.Find h′(3).Possibilities:(a) 6(b) 10(c) 12(d) 14(e) 155. Suppose that f(x) = 2√x2+ 1. Find the limitlimh→0f(3 + h) −f(3)h.(Hint: Relate the limit to a derivative.)Possibilities:(a) 3/√10(b) 4/√10(c) 5/√10(d) 6/√10(e) 7/√106. Find the equation of the tangent line to the graph of f(x) = x3− 6x + 2 at x = 2.Possibilities:(a) y = 6x − 14(b) y = 5x + 8(c) y = 7x − 16(d) y = 8x + 10(e) y = −6x + 1047. Find the maximum value of f(x) = x3+ 3x2− 9x + 8 on the interval [−4, 2].Possibilities:(a) 33(b) 34(c) 35(d) 36(e) 378. Find the interval(s) where f(x) = x3+ 3x2− 9x + 8 is decreasing.Possibilities:(a) (−∞, −3) and (1, ∞)(b) (−∞, −1) and (3, ∞)(c) (−3, 1)(d) (−1, 3)(e) (0, ∞)9. Suppose that Q(t) = Q0ert. Assume that (0, 3) lies on the graph of Q(t). Assume also that the slopeof the tangent line to the graph of Q(t) at t = 0 is 36. Find r.Possibilities:(a) 24(b) 8.5(c) e(d) 12(e) 8e510. Suppose that g(x) =1f(x)and the equation of the tangent line to the graph of f(x) at x = 3 isy = 2 + 8(x −3). Find g′(3).Possibilities:(a) 1(b) −2(c) 2(d) 0(e) −111. Assume that f(x) = xe−x. Find f′′(2).(a) e2(b) e−2(c) −e−2(d) 2e(e) 012. Find the maximum of g(t) = |t + 4| − 4 on the interval [−20, 10].Possibilities:(a) 12(b) 14(c) 16(d) 18(e) 20613. If the number of bacteria in a culture doubles in 3 hours, how many hours will it take be fore 5times the original number is present.Possibilities:(a) 15/ 2(b) 5/2(c) 5/3(d) 3 ln 5/ ln 2(e) 3 ln 2/ ln 514. Suppose that g(x) = x2− 4x + 7. Find a value c in the interval [2, 6] such that g′(c) eq ua ls theaverage rate of change of g(x) on the interval [2, 6].Possibilities:(a) 0(b) 1(c) 2(d) 3(e) 415. Find a value of x where the function f(x) = x ln x has a minimum.Possibilities:(a) 1/e(b) e(c) 1(d) 1/2(e) f (x) has no
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