MA 123 — Elementary CalculusSECOND MIDTERM EXAMSpring 201003/10/2010Name: 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 e xam 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 e ach corre ct 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 MIDTERM EXAMSpring 2 01003/10/2010Please 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 M. Shaw MWF 12:00 pm - 12:50 pm, CP 153002 T. Chapman MWF 2:00 pm - 2:50 pm, CP 139003 P. Koester TR 12:30 pm - 1:45 pm, CP 153004 M. Shaw MWF 9:00 am- 9:50 am, BS 116005 P. Koester MWF 1:00 pm - 1:50 pm, CB 122D. Moore T 11:00 am - 12:15, CB 303006 P. Koester MWF 1:00 pm - 1:50 pm, CB 122J. Polly R 11:00 am - 12:15, DH 301007 P. Koester MWF 1:00 pm - 1:50 pm, CB 122D. Moore T 9:30 am - 10:45, CB 243008 P. Koester MWF 1:00 pm - 1:50 pm, CB 122J. Polly R 9:30 am - 10:45, CB 243009 D. Leep MWF 10:00 am - 10:50 am, CP 320A. Barra T 1:00 pm - 2:15, CP 397010 D. Leep MWF 10:00 am - 10:50 am, CP 320A. Barra R 1:00 pm - 2:15, CB 304011 D. Leep MWF 10:00 am - 10:50 am, CP 320A. Barra T 2:30 pm - 3:45, CP 246012 D. Leep MWF 10:00 am - 10:50 am, CP 320A. Barra R 2:30 pm - 3:45, CP 235013 A. Corso MWF 12:00 pm - 12:50 pm, CB 110401 D. Little TR 6:00 pm-7:15 pm, CB 339402 D. Little 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. Find the instantaneous rate of change of h(x) at x = 4, whereh(x) =√73 − x3Possibilities:(a) −8(b) −6(c) −4(d) 2(e) 42. Supposef(x + h) − f(x)h=3h2− 4xhh√x2+ 8Find the slope of the tangent line to y = f (x) at x = 1Possibilities:(a) 0(b)3h − 43(c) −19h +3227(d) −49(e) −433. Suppose f(x) = (x − 6)2andf(x + h) − f(x)h= Ax + Bh + Cfor some numbers A, B, and C. Determine C.Possibilities:(a) −6(b) 6(c) 0(d) −12(e) 1234. The graph of the function f(x) (solid) and its tangent lin e (dotted line) at x = −1 are given.Find f0(−1).Possibilities:(a) −1(b) −2(c) 2(d) 3(e) 45. The tangent line to the graph of g(x) at x = −1 is given by y = 4(x + 1) + 7. SupposeF (x) = x3g(x)Find F0(−1).Possibilities:(a) 25(b) 17(c) −4(d) 4(e) −176. Let h(x) = 7 + ln(x2− 3x − 3). Find the equation of the tangent line to h(x) at x = 4.Possibilities:(a) y =14x + 6(b) y =14x + 4(c) y = 5x − 13(d) y = x + 4(e) y = 5x − 1247. Find g0(2) whereg(x) =x + 2x2+ 1Possibilities:(a)1125(b) −1125(c)115(d) −115(e)358. Let F (x) = e8x. Find the 10th d erivative, F(10)(x).Possibilities:(a) e8x(b) 0(c) e80(d) 108e8x(e) 810e8x9. f (x) = x + e−x. Find f0(30).Possibilities:(a) 1 − 30e−31(b) 1 − 30e−29(c) 1 − e−30(d) 1 + e−30(e) 1 + 30e−30510. Suppose G(x) = h(4x), a nd h(3) = 2, h0(3) = −3, h(4) = 4, h0(4) = 6, h(12) = 8, and h0(12) = −1.Find G0(3).Possibilities:(a) −8(b) −4(c) −1(d) 6(e) 811. Q(t) = t3. Find a number c in the interval (1, 3) so that the average rate of change of Q(t) on [1, 3]is equal to the instantaneous rate of change at t = c.Possibilities:(a)√13(b)2√3(c)r132(d)133(e)r13312. Find the number c in the interval [−2, 3] so that the minimum of f (x) = x3− 6x2− 15x − 4 on theinterval [−2, 3] occurs at x = c.Possibilities:(a) −104(b) −76(c) −1(d) 3(e) 5613. Supposeg(x) =(2x2, x ≤ 04x, x > 0Find the maximum value of g(x) on the interval [−4, 2].Possibilities:(a) f (x) does not have a maximum on [−4, 2](b) −4(c) 8(d) 32(e) 3814. How much money must be invested now in order to have $3, 000 in 5 years, assuming interest iscompounded continuously at an annual rate of 6%?Possibilities:(a) 3000 e−0.3(b) 3000 e−3(c) 3000 e−30(d) 3000 e0.3(e) 3000 (1.06)−515. Suppose g(x) = a ebxfor some constants a and b. Suppose (0, 2) is on the graph of y = g(x).Also, suppose g0(0) = −6. Find g(1).(Hint: use the two given conditions to d etermine a and b, then find g(1).)Possibilities:(a) 2e−3(b) 2e3(c) −2e6(d) −6(e)
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