Find the following

Question

Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns.

Centerville is located at (11,0) in the xy-plane, Springfield is at (0,3), and Shelbyville is at (0,-3). To save on the cost of cable, Greedy Cablevision wants to arrange the cable in a Y-shaped configuation, running cable from Centerville to some point (x,0) on the x-axis where it then splits into two branches, one going to Springfield and one to Shelbyville.

Find the location (x,0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your conclusion by answering the following questions.

(a) To solve this problem we need to minimize the following function of x:

f(x)=

b) we find that f(x) = critical point at

x=

c) to verifty f(x) has a minimum at this critical point we evalute the second derivative f''(x) at this point

f''(critical point is , positive number

d) thus the minimu length of cable needed is

Answer 1

f(x) = √[(11 - x)² + y²] + √[x² + (y - 3)²] + √[x² + (y + 3)²], that is "a" now you finsh.