8. The function fhas the property that f(x), f'(x), and f" (x) are negative for all values of x. Which of the following could be the graph of f? a) b) A C) d) e)9. The graph of a piecewise-linear function f, for -1x4, is shown below. What is the value of | f (x) dx ? Y O -1 a) 1 b) 2.5 c) 4 d) 5.5 e) 817. Which of the following is the solution to the differential equation dy 3x2 with dx V the initial condition y (3) = -2? a) y = 2et b) y = 2ex-27 c)y=x - 25 d) y = v2x' -50 e) y = -V2x3 -50 18. Let g be a twice-differentiable function with g'(x) > 0 and g"(x) >0 for all real numbers x, such that g (4) =12 and g (5) =18. Of the following, which is a possible value for g (6)? A) 15 B) 18 C) 21 D) 24 E) 2732. The function fis continuous on the closed interval 2 x 8 and has values as given in the table below. Using the subintervals [2, 5], [5.7] and [7,8]. 100 approximate f (x) dx using a left-hand approximation with three rectangles. 2 5 7 f (x) 10 30 40 20 a) 110 b) 130 c) 160 d) 190 e) 21035. Suppose that a five-year rate of projection growth of population trends suggests that t years from now, the population of a certain community will be P thousand. where P(t) =-+ +912 + 48t + 200 At what time will the RATE of population growth be maximized? a) t = 3years b) t = 13 years c) t =15 years d) t = 60 years e) t = 75 years36. It is projected that t months from now, the average price per unit for goods in a certain sector of the economy will be P dollars where P(t) = 43 +7:2 +200r+300 At what rate will the rate of Brice increase be changing with respect to the time 5 months 'om now? b) $195 unit per month b) $ 1 6 unit per month per month c) $2.33 unit per month per month :1) $10.83 unit per month per month e) $10 unit per month per month 38. The temperature of a cup of hot chocolate changes at the rate of r(r) = e_'12'C per minute with t measured in minutes. Calculate the change in the temperature ow 1' = 0 to t = 3 minutes. decreases 15.116DC decreases 1.814" C decreases 0.502"C decreases 0.?20"C decreases 10.720C 40. The rate at which people enter an amusement park on a given day is modeled by the function E defined by E(t ) =7 15600 (f- - 241+160 E (t) is measured in people per hour and time t is measured in hours after midnight. The function is valid for 9 t