Centerville is located at (8,0) in the xy-plane, Springfield is at (0,5), and Shelbyville is at (0,-5). 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. The following diagram is useful: f(x)=x-8+2√x² +25 (b) We find that f(x) has a critical point at Springfield (0,5) Shelbyville (0,5) x= (,0) (a) To solve this problem we need to minimize the following function of x: (Click on the graph to enlarge it.) Centerville (8,0) 5√3 3 (c) To verify that f(x) has a minimum at this critical point we evaluate the second derivative f"(x) at this point.

Centerville is located at (8,0) in the xy-plane, Springfield is at (0,5), and Shelbyville is at (0,-5). 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. The following diagram is useful: f(x)=x-8+2√x² +25 (b) We find that f(x) has a critical point at Springfield (0,5) Shelbyville (0,5) x= (,0) (a) To solve this problem we need to minimize the following function of x: (Click on the graph to enlarge it.) Centerville (8,0) 5√3 3 (c) To verify that f(x) has a minimum at this critical point we evaluate the second derivative f"(x) at this point.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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