Problem 2. The curved roof of a new building is constructed by a thin shell structure. To avoid curved walls and ceilings in the interior of the building, a room (with vertical walls and a horizontal ceiling) should be constmcted so that it has the maximum possible volume that ts beneath the roof. One possible example (in which the volume of the room is not the maximum possible one) is depicted in Fig. 1a). As can be seen, the curved roof does not change in the z-direction. Consequently, the 3D problem reduces to the 2D problem of nding the maximum possible rectangular area Arec under the curve given by the function _ 1 1 f(x) = Ecosx x\" + 3, which describes the roof in the x- y plane, see Fig. 1b). a) Use the bisection method with the tolerance a = 0.3 to nd a reasonable approximation 62 of the positive root at of f (x) in the initial interval [2, 3] (use hand calculations to perform the calculations). Based on this result, what is the maximum possible length of the rectangle l? Figure 1: a) Curved roof in 3D with room beneath it, b) 2D description of the problem. b) Turn the problem of nding the maximum possible rectangular area Amc under f (x) into a new rootnding problem of the form g(x) = 0. Use Newton's method with the initial guess x0 = 62, where 65 is the approximated root found in Part a), and two iterations to nd an approximation of the positive root ,8 of g(x) in the interval [0, 07] (use hand calculations to perform the calculations). Based on this result, what is the maximum possible area of the rectangle Am