4. Which of (I)-(V) are antiderivatives of f(x) = 1/x? I. In x II. - 1/x2 III. In x + In 3 IV. In (2x) V. In (x + 1)In Exercises 6-21, find an antiderivative.10. g(2)t2 + 1 20. f(t)4. Let G'(t) = g(t) and G(0) = 4. Use Figure 6.12 to find the values of G(t) at t = 5, 10, 20, 25. + N -g (1) 10 15 20 -2 Figure 6.12In Exercises 5-12, sketch two functions F such that F" = f. In one case let F(0) = 0 and in the other, let F(0) = 1.\f14. Let F(x) be an antiderivative of f(x), with F(1) = 20 and ff f(x) da = -7. What is F(4)?Problems 18-21 show the function f whose antiderivative F has F(0) = 0. Find the value of c that makes F(5) = 0. f (1) C 2 -16 18.28. Figure 6.17 shows the rate of change of the concentration of adrenaline, in micrograms per milliliter per minute, in a person's body. Sketch a graph of the concentration of adrenaline, in micrograms per milliliter, in the body as a function of time, in minutes. rate of change of adrenaline concentration (ug/ml/min) 12 - 1 (minutes) Figure 6.1739. The Quabbin Reservoir in the western part of Massachusetts provides most of Boston's water. The graph in Figure 6.23 represents the flow of water in and out of the Quabbin Reservoir throughout 2016. a. Sketch a graph of the quantity of water in the reservoir, as a function of time. b. When, in the course of 2016, was the quantity of water in the reservoir largest? Smallest? Mark and label these points on the graph you drew in part (a). Answer c. When was the quantity of water increasing most rapidly? Decreasing most rapidly? Mark and label these times on both graphs. > Answer d. By July 2017 the quantity of water in the reservoir was about the same as in January 2016. Draw plausible graphs for the flow into and the flow out of the reservoir for the first half of 2017. rate of flow (millions of gallons/day) Outflow Inflow Jan (2016) April July Oct Jan (2017) Figure 6.2342. Figure 4.80 shows graphs of four members of the family Are " + Brel f(x) = a. What value does f(x) approach as x - co? As x - -co? b. Explain the graphical significance of A and B. c. Which graph corresponds to each pair of values for (A, B): (2, 1), (-1,2), (-2,0), (-1,-2)? (1) (II) (III) 200 + (IV) 200+ 200 + 200 + + x + x + X -100 100 -100 + x 100 -100 -200 -200 100 -100 100 -200 -200 Figure 4.8066. The force, F, on a particle with potential energy U is given by Using the expression for U in Problem 65, graph Fand U on the same axes, labeling intercepts and local maxima and minimal