x ) -+x+1. [-2. 1]12. - I\f30. V = lan X. - 232.\f56. Solve Exercise 55 when CD = 2 cm.46. Suppose that f is continuous on [0. 4]. f(0) = 1, and 2 6 /'(x) s 5 for all x in (0. 4). Show that 9 s f(4) = 21.87. A light is to be mounted atop a pole of height h fect to illuminate a busy traffic circle, which has a radius of 40 IL. The intensity of illumination / at any point P on the circle is directly proportional to the cosine of the angle # (sec the figure) and inversely proportional to the square of the distance d from the source. (a) How tall should the light pole be to maximize / (b) Suppose that the light pole is h feet tall and that a woman is walking away from the base of the pole at the rate of 4 ft/s. At what rate is the intensity of the light at the point on her back 4 ft above the ground decreasing when she reaches the outer edge of the traffic circle?60. A manufacturer determines that the cost of making :1: units of a commodity is C(m) = 1800 + 25x 0.2m2 + 0.001m2 and the demand furiction is p(ac) = 48.2 0.0.393. (a) Graph the cost and revenue functions and use the graphs to estimate the production level for maximum provit. (b) Use calculus to nd the production level for maximum prodic. (c) Fstimate the production level that minimizes the average cost