Exam II Review Packet MATH 127Math 127EXAM II REVIEW PACKETSPRING 20121. Let a and b be constant, find the derivative of W (q) = 3ab2q(a) W0(q) = 6ab(b) W0(q) = 3ab2(c) W0(q) = 6abq(d) W0(q) = 02. Findddx[3√x2(x + 1)].(a)53√x22+3√x2(b)23√x3+ 1(c)53√x23+233√x(d)3√x5+3√x23. Let P (t) =r1t3− 3t, find P0(1).(a) −4.80(b) −6.30(c) 1.80(d) −2.414. Let f(t) = 2t3− 4t2+ e−0.5t, find f00(t).(a) 12t − 8 − 0.5e−0.5t(b) 12t − 8 + e−0.5t(c) 6t2− 8t − 0.5e−0.5t(d) 12t − 8 + 0.25e−0.5tExam II Review Packet – 2 – MATH 1275. Find the relative rate of change of function f(x) = 5e1.5x. (Hint:ddx[ln(f(x))])(a) 0.5(b) 1.0(c) 1.5(d) 2.06. Given Q(t) =√et+ π3, find the slope of the line tangent to Q(t) at the point t.(a)et2(et+ π3)−1/2(b)et+ 3π22(et+ π3)−1/2(c)et+ 12(et+ π3)−1/2(d)12(et+ π3)−1/27. Let W (y) =3y + y25 + y, find W0(y).(a)−y2− 10y − 15(5 + y)2(b)y2+ 10y + 15(5 + y)2(c)3 + 2y(5 + y)2(d)y2+ 2y − 5(5 + y)28. Given a power function of the form f (x) = axn, with f0(2) = 3 and f0(4) = 24, find n and a. [Hint: (I)Findf0(4)f0(2); (II) Use power rules such as 4x= 22x, and343= 33.](a) n = 2, a = 1/32(b) n = 2, a = 3/32(c) n = 4, a = 1/32(d) n = 4, a = 3/32Exam II Review Packet – 3 – MATH 1279. Given the function f(x) = xeax, find a such that the function f(x) has a critical point at x = 3.(a) a = 0(b) a = −1/3(c) a = 1(d) a = 3/410. Given f(x) = x − 2 ln(x), find all local minima and maxima where x > 0.(a) Local maximum at x = 2(b) There are no local maxima or minima(c) Local minimum at x = 2(d) Local maximum at x = 1 and local minimum at x = 211. Given the graph of f0(x) below, which of the following statement is TRUE?(a) f has 2 critical points; a is local maximum and g is local minimum(b) f has 3 critical points; b and f are local maxima and d is local minimum(c) f has 2 critical points; e is local maximum and c is local minimum(d) f has 2 critical points; c is local maximum and e is local minimum12. Given U(x) =23x3+ bx2+ cx with critical points at x = −1 and x =12, and inflection point at x = −14.Find b and c.(a) b = −1/2, c = −1(b) b = 1/2, c = 1(c) b = 1/2, c = −1(d) b = −1/2 , c = 1Exam II Review Packet – 4 – MATH 12713. Suppose f has a continuous derivative whose values are given in the following table, which of the followingstatement is FALSE?x 0 1 2 3 4 5 6 7 8 9 10f’(x) 5 2 1 -2 -5 -3 -1 2 3 1 -1(a) There is a local maximum between x = 2 and x = 3(b) There is a local maximum between x = 7 and x = 9(c) There is a local minimum between x = 6 and x = 7(d) There is a local maximum between x = 9 and x = 1014. Find the points of inflection of f(x) = x4− 24x2+ 1.(a) (2, −79) and (−2, −79)(b) (2, 65) and (−2, −79)(c) (2, 79) and (−2, −65)(d) (2, −79) and (−2, 65)15. Given g(x) = −x4+ 2x3+ 1, find the global minimum and global maximum values with domain [−1, 2].(a) Global maximum at x = 2 and global minimum at x = 0 and x = 1.(b) Global maximum at x = 1.5 and global minimum at x = 0 and x = 1.(c) Global maximum at x = 2 and global minimum at x = −1(d) Global maximum at x = 1.5 and global minimum at −116. At a price of $4 per frozen yogurt, demand is 900 units. Every decrease of one dollar, the demand increasesby 200 units. What price maximizes revenue?(a) 640(b) 850(c) 4.25(d) 8.5017. A landscape architect plans to enclose a rectangular area against a wall. Find the maximum area that a880−foot fence can enclose.(a) 96, 800(b) 76, 200(c) 106, 000(d) 54, 400Exam II Review Packet – 5 – MATH 12718. Revenue is given by R(q) = 450q and cost is given by C(q) = 10, 000 + 3q2. At what quantity is profitmaximized? What is the total profit at this production level?(a) q = 75, π = 40, 625(b) q = 75, π = 6, 875(c) q = −75, π = 6, 875(d) q = −75, π = −60, 62519. A population, P , growing logistically is given by P (t) =401 + 11e−0.08t, where t is in years. What is the timet when the population P growing the fastest? Round your answer to the nearest year.(a) 24(b) 26(c) 28(d) 3020. If time, t, is in seconds and concentration, C, is in ng/ml, the drug concentration curve for a drug is givenby C(t) = 16.8te−0.8t. What is the amount of concentration when the drug reaches its peak concentration?(a) −1.25(b) 1.25(c) 7.725(d) 6.18021. Find the intersection point of the following two lines (Line A and Line B): Line A is tangent to y = x3atx = 2, and Line B is tangent to y = 2x2at x = 1. (*This type of question appeared on last year’s exam*)(a) (7/4, 5)(b) (5, 7/4)(c) (4/7, 1/5)(d) (1/5, 4/7)ANSWER SHEET FOLLOWSANSWER SHEET – 6 – MATH 1271. B2. C3. A4. D5. C6. A7. B8. D9. B10. C11. D12. C13. B14. A15. D16. C17. A18. B19. D20. C21. ANote: In problem 2, if you use product rule, your answer should be2(x + 1)3x1/3+ x2/3, which is the same asanswer c but in different