MA 123 — Elem. CalculusSECOND MIDTERMSPRING 200703/07/2007Name: 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 15 multiple choice q uestions. Record your answers on this page by filling in thebox corresponding to the correct answer. For example, 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 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.abcdeFor grading use:Total(out of 100 pts)1MA 123 — Elem. CalculusSECOND MIDTERMSPRING 200703/07/2007Name:Sec.:Please make sure to list the correct section number on the front page of your exam and on this page.In case you forgot your section number, consult the following table:Section # Instructor Lectures001 J. Robbins MWF 12:00pm-12:50pm, BS 107002 P. Perry MWF 2:00pm-2:50p m , CB 118003 J. Robbins TR 3:30pm-4:45pm, CB 337401 S. Speakman MW 7:30pm-8:45pm, CB 339402 N. Kirby TR 6:00pm-7:15pm, 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. Let k(x) = (x + 3)(x + 4)(x + 1). Find k′(x).Possibilities:(a) 12(b) 3x2+ 16x + 19(c) 3x2+ 18x + 20(d) 3x2+ 14x + 16(e) 12. Let f(x) = 3x2+ 6x + 4. Find the maximum value of f (x) on the interval [−2, 1].Possibilities:(a) 5(b) 7(c) 9(d) 13(e) −13. If f(x) = 6x2+ 3x − 1, find f′(x).Possibilities:(a) 6x + 1(b) 12x + 3(c) 12x − 1(d) 2x + 3(e) 2x + 534. Suppose F (x) = g(h(x)). If g(2) = 3, g′(2) = 4, h(0) = 2 and h′(0) = 6, find F′(0).Possibilities:(a) 12(b) 4(c) 24(d) 6(e) 35. If f(s) = (s2+ 5s + 4)3, find f′(s).Possibilities:(a) 3(s2+ 5s + 4)2(b) 3(s2+ s + 4)2(c) 2(s2+ 5s + 4) · (2s + 5)(d) 3(s2+ s + 4)2· (2s + 1)(e) 3(s2+ 5s + 4)2· (2s + 5)6. If f(x) = | x − 1| findlimh→0f(1 + h) − f (1)hPossibilities:(a) 3(b) −3(c) 1(d) −1(e) Does not exist47. If f(x) = (x + 6)2, findf(x + h) − f (x)hPossibilities:(a) 2x + 2h + 12(b) 2x + h − 2(c) 2x + 2h + 2(d) 2x + h + 12(e) 2x + h − 128. Find Y′(s) if Y (s) =14s2−5s.Possibilities:(a)52s−3+ s−2(b) −12s−3+ 5s−2(c) −25s−3+ s−2(d)12s−3+ 5s−2(e) −2s−3− 3s−29. Suppose k(s) = s2+ 3s + 1. Find a value c in the interval [1, 3] such that k′(c) equals the averagerate of change of k(s) on the interval [1, 3].Possibilities:(a) −1(b) 0(c) 1(d) 2(e) 3510. Suppose h(x) = [f(x)]2and the equation of the tangent line to the graph of f(x) at x = 1 isy = 3 + 4(x − 1). Find h′(1).Possibilities:(a) 28(b) 40(c) 14(d) 24(e) 2011. LetG(x) =((x − 3) + 6 if x ≥ 3−(x − 3) + 6 if x < 3Find the minimum of G(x) on the interval [−10, 10].Possibilities:(a) 3(b) 1(c) −6(d) 19(e) 612. Suppose that a function f(x) has derivative f′(x) = x2+ 1. Which of the following statements istrue about the graph of y = f(x)?Possibilities:(a) The function is increasing on (−∞, ∞).(b) The function is decreasing on (−∞, ∞).(c) The funtion is increasing on (−∞, −1) and (1, ∞), and the function is decreasing on (−1, 1).(d) The function is increasing on (−∞, 0), and the function is decreasing on (0, ∞).(e) The function is decreasing on (−∞, 0), and the function is increasing on (0, ∞).613. Suppose u(t) and w(t) are differentiable for all t and the following values of the functions andderivatives are known: u(7) = 2, u′(7) = −1, w(7) = 1, and w′(7) = 9. Find the value of h′(7) whenh(t) =w(t) + 5u(t).Possibilities:(a) 3(b) 6(c) −3(d) 12(e) −614. Suppose that a function h(x) has derivative h′(x) = x2+ 4. Find the x value in the in terval [−1, 3]where h(x) takes its minimum.Possibilities:(a) −1(b) 3(c) 5(d) 13(e) 2915. Let f(x) = 2x. Use a calculator and the definition of the derivative as a limit to estimate the valueof f′(1).Possibilities:(a) 1.386(b) 2.296(c) 4.768(d) 5.545(e)
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