MA123 Exam 2March 5 2008NAME ____________________________ Section __________Problem Answer123456789101112131415a b c d ea b c d ea b c d ea b c d ea b c d ea b c d ea b c d ea b c d ea b c d ea b c d ea b c d ea b c d ea b c d ea b c d ea b c d eInstructions. Circle your answer in ink on the page containing the problemand on the cover sheet. After the exam b egins , you may not ask a questionabout the exam. Be sure you have all pages (containing 15 problems) beforeyou begin. For grading use:Number of problems correct: ________/15SCORE: ________/1001NAME_______________________________________________________1. If f(x) =−xx2−1then f0(x) =(a)−x2−1(x2−1)2(b)12x(c)−x2−1x2−1(d)x2+1x2−1(e)x2+1(x2−1)22. If F (s) =√2s + 2, find F0(1).(a)12(b)12√2(c)1√2(d)32√2(e)323. If g(t) =1t2+1, then the slope of the tangent line to the graph of g(t) att = 3 is(a) −125(b) −225(c) −150(d) −350(e) −42524. If R(x) = (x − 2)(x2− 2)(x3− 2), find R0(2).(a) 0(b) 12(c) 48(d) −8(e) −65. Suppose f(t) = H(G(t)) and H(3) = 5, H0(3) = 4, G(2) = 3, andG0(2) = 7. Find f0(2).(a) 12(b) 35(c) 28(d) 15(e) 436. If G(s) = u(s2) and u(1) = 10, u0(1) = 4, u(−1) = 7, and u0(−1) = 2,then G0(−1) =(a) −20(b) 4(c) 10(d) 2(e) −837. Let f(x) = |x2−1|+ 2. Find the minimum of f(x) on the interval [−3, 3].(a) 3(b) 0(c) 1(d) 2(e) −18. Let Q(t) = t2. Find a value A such that the average rate of change of Q(t)from 1 to A equals the instantaneous rate of change of Q(t) at t = 2A.(a) 1(b)13(c)14(d)15(e) Does not exist9. Suppose the derivative of a function g(x) is given by g0(x) = x2−1. Findall intervals on which g(x) is increasing.(a) (−∞, ∞)(b) (−1, 1)(c) (−∞, −1) and (1, ∞)(d) (0, ∞)(e) (−∞, 0)410. Suppose f(t) = 2t3− 9t2+ 12t + 31. Find the value of t in the interval[0, 3] where f (t) takes on its minimum.(a) 0(b) 1(c) 2(d) 3(e) Neither the maximum nor the minimum exists on the given interval.11. Suppose that f(x) = xg(x), and for all positive values of x the functiong(x) is negative (i.e., g(x) < 0) and decreasing. Which of the following istrue for the function f(x)?(a) f (x) is negative and decreasing for all positive values of x.(b) f (x) is positive and increasing for all positive values of x.(c) f (x) is negative and increasing for all positive values of x.(d) f (x) is positive and decreasing for all positive values of x.(e) None of the above12. If Q(s) = s7+ 1, findlimh→0Q(1 + h) − Q(1)h(a) 2(b) 5(c) 6(d) 7(e) 8513. Suppose f(t) =F (t)tand F (1) = 2, F0(1) = 6. Find f0(1).(a) 2(b) 4(c) 1(d) −4(e) −114. If the line y = 9 + 3(x − 4) is tangent to the graph of G(x) at x = 4 andG(x) is differentiable at x = 4, then G(4) − G0(4) equals(a) 3(b) 4(c) 5(d) 6(e) 915. Suppose the derivative of H(s) is given by H0(s) = s2(s + 1). Find thevalue of s in the interval [−100, 100] where H(s) takes on its minimum.(a) −100(b) −1(c) 0(d) 1(e)
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