MA 123 — Elem. CalculusEXAM 2Fall 201010/20/2010Name:Sec.:Do not remove this answer page — you will turn in the entire exam. You have two hours to do thisexam. No books or notes may be used. You may use a graphing calculator during the exam, but NOcalculator with a Computer Algebra System (CAS) or a QWERTY keyboard is permitted. Absolutelyno cell phone use during the exam is allowed.The exam consists of multiple choice questions. Record your answers on this page. For each multiplechoice question, you will need to fill in the box corresponding to the correct answer. For example, if (b)is correct, you must writeabcdeDo not circle a nswers on this page, but please circle the letter of ea ch correct response in the body ofthe exam. It is your responsibility to make it CLEA R 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.abcde16.abcde17.abcde18.abcde19.abcde20.abcdeFor grading use:NumberCorrect(out of 20 problems)Total(out of 100 points)1MA 123- Elem. CalculusEXAM 2Fall 201010/20/2010Please make sure to list the correct section number on the front page of your exam. In case you forgotyour section number, consult the following table. If you are enrolled in a lecture with recitation, thenyour section number is determined by your recitation time and location.Section # Instructor Lectures001 T. Chapman MWF 8:00 am - 8:50 am, CB 118002 D. Leep MWF 12:00 pm - 12:50 pm, KAS 213003 M. Shaw TR 8:00 am - 9:15 am, CP 155004 J. Schmidt TR 12:30 am- 1:45 am, CP 155005 M. Music T 3:30 pm - 4:45 pm, CP 345006 M. Music R 3:30 pm - 4:45 pm, CP 208007 W. Robinson T 3:30 pm - 4:45 pm, CP 208008 W. Robinson R 3:30 pm - 4:45 pm, CB 204009 M. Music T 12:30 pm - 1:45 pm, NURS 214010 W. Robinson R 12:30 pm - 1:45 pm, NURS 504011 S. Taylor T 9:30 am - 10:45 am, BE 248012 S. Taylor R 9:30 am - 10:45 am, CB 214013 B. Fox T 9:30 am - 10:45 am, MMRB 243014 B. Fox T 9:30 am - 10:45 am, FB B3015 C. Taylor T 11:00 am - 12:15 pm, CB 347016 B. Fox T 11:00 am - 12:15 pm, CB 243017 C. Taylor T 2:00 pm - 3:15 pm, NURS 511018 C. Taylor R 2:00 pm - 3:15 pm, DH 323019 G. Tiser T 2:00 pm - 3:15 pm, CB 213020 S. Taylor R 2:00 pm - 3:15 pm, FB B8021 G. Tiser T 12:30 pm - 1:45 pm, FPAT 255022 G. Tiser R 12:30 pm - 1:45 pm, DH 323401 S. Foege TR 6:00 pm-7:15 pm, CB 347402 S. Foege TR 7:30 pm-8:45 pm, CB 3472Multiple 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. The graph of y = g(x) is shown, as well as the tangent line to the graph at x = 1. Determine g′(1).-3 -2 -1 0 1 2 3 4-3-2-1012345xyPossibilities:(a) 1(b) 2(c) −2(d) 1/2(e) 02. f(x) = (x −6)2. Find the value of C, given thatf(x + h) − f(x)h= Ax + Bh + CPossibilities:(a) −12(b) −11(c) −10(d) −9(e) −833. Find the equation of the tangent line to the graph of y = x3− 4x2− 2x + 4 at x = 3.Possibilities:(a) y = −x − 8(b) y = −11(c) y = x − 14(d) y = 2x − 17(e) y = 3x − 204. Find the equation of the tangent line to the graph of f(x) =√x + 5 at x = 4.Possibilities:(a) y = (1/4) x + 3(b) y = (1/4) x + 4(c) y = (1/4) x + 5(d) y = (1/4) x + 6(e) y = (1/4) x + 75. Suppose thatf(x + h) − f(x)h=−8hx − 4h2hFind the derivative, f′(2).Possibilities:(a) −16 −4h(b) −16(c) 0(d) −8(e) The derivative does not exist.46. Find the derivative, f′(x), off(x) =1x7Possibilities:(a) −7x−6(b) 1/(7 x8)(c) 1/(7 x6)(d) 7x6(e) −7x−87. Suppose f(3) = 4, f′(3) = 9, g(3) = 2, g′(3) = 3, g(−3) = −5, and g′(−3) = 5.Find F′(3), given thatF (x) = f(x)g(x)Possibilities:(a) 35(b) 30(c) 27(d) 42(e) There is not enough information to find the requested derivative.8. Find the derivative, f′(x), wheref(x) =x + 5x + 4Possibilities:(a) 1/(x + 4)(b) −1/(x + 4)(c) −1/ (x + 4)2(d) 1(e) 1/ (x + 4)259. Find the derivative, f′(x), wheref(x) = ln7x2+ 5x + 7Possibilities:(a)17x2+ 5x + 7(b) 14x + 5(c)14x + 57x2+ 5x + 7(d)114x + 5(e)7x2+ 5x + 714x + 510. Find the de rivative, f′(2), wheref(x) =√21 + x2Possibilities:(a) 2/5(b)√5/5(c) 4/5(d) 2√5/5(e) 1/511. Find the de rivative, f′(x), wheref(x) = x6ln (x)Possibilities:(a) x6(b) 6x5ln (x) + x6(c) 6x5(d) 6x5ln (x) + x5(e) 6x4612. Find the 11thderivative, f(11)(x), wheref(x) = e10xPossibilities:(a) 1011e10x(b) 1110e10x(c) e10x(d) e110(e) 013. Find the de rivative, f′(34), wheref(x) = 5x + e−xPossibilities:(a) 5 −e−34(b) 5 − 34e−33(c) 5 + 34e−34(d) 5 + e−34(e) 5 −34e−3514. Suppose g(2) = 2 and g′(2) = −3. Find F′(2), given thatF (x) = (g(x))4Possibilities:(a) −192(b) −96(c) 32(d) −24(e) 24715. Find the second derivative, f′′(x), wheref(x) = ex2Possibilities:(a) 4x2ex2(b) 2xex2(c) 4xex2(d) 2ex2+ 4x2ex2(e) 2xex2+ 4x2ex216. How much money must be invested now in order to have $3500 in 6 years, assuming interest iscompounded continuously at an annual rate of 4.0 % ?Possibilities:(a) 3500e24.0(b) 3500e−24.0(c) 3500e.240(d) 3500(1 + 0.04)−6(e) 3500e−.24017. The population of a certain country triples every 37 years. If we express the population asP (t) = P0er·t, then find r.Possibilities:(a) 37/ ln (3)(b) 37 ln (3)(c) 3/ ln (37)(d) ln (3) /37(e) ln (37) /3818. Find the maximum value of f(x) on [−5, 4] where f (x) = |x − 1| + 16.Possibilities:(a) 22(b) 19(c) 1(d) −5(e) 1619. Find the value of x in the interval [0, 6] where f (x) = 2x3− 21x2+ 60x + 8 attains its maximumvalue.Possibilities:(a) 60(b) 2(c) 5(d) 0(e) 820. Let f(t) = t3. Find a value c in the interval (7, 10) so that the average rate of change of f(t) on[7, 10] is equal to the instantaneous rate of change of f(t) at t = c.Possibilities:(a) 219/2(b) 73(c)p(219/2)(d)