19. A road is to be built between two cities C, and C, which are on opposite sides of a river of uniform width r. C, is a units from the river and C, is b units from the river, with a s b. A bridge will carry the traffic across the river. Where should the bridge be located in order to minimize the total distance between the cities? Give a general solution using the constants a, p-x b, p, and r as shown in the figure. Bridge-I River P Find D(x), the total distance between the cities. Choose the correct answer below. O A. D(x) = Val + (p-x)2 + vb?+x2 OB. D(X) = Val + (p-x)2 +b2 +x2 +r O c. D(x) = Vaz + (p-x)? +r OD. D(x) = Vb? + x2 +r To find the critical value(s), first find D'(x). Choose the correct answer below. x- p X p - x O A. D'(x) = 162 + x2 OB. D'(x) = Vaz + (p -x)2 b2 + x2 Vaz + (p - x) 2 P - x p - > O c. D'(x) = (b2 - x2 OD. D'(x) = Vaz - (p -x)2 b2 + x2 Vaz + (p - x)2 For what values of x, if any, does D'(x) = 0? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. X= (Use a comma to separate answers as needed.) O B. There are no such values of x. For what values of x, if any, does D'(x) not exist? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. *= (Use a comma to separate answers as needed.) O B. There are no such values of x. The critical value is x = - bp atb . Use the second derivative to determine whether it corresponds to a minimum. bp Consider x = - "atb. Which of the following describes D" 3 +62 OA. D = bp a +b 0 O C. D bp =0 Suppose that f is differentiable for every x in an open interval (a,b) and that there is a critical value c in (a,b) for which f'(c) = 0. Then the Second-Derivative Test says that f(c) is a relative minimum if f"(c) > 0 and f(c) is a relative maximum if f"(c)