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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. The idea is to save on the cost of cable by arranging the cable in a Y-shaped configuation. Centerville is located at (12, 0) in the ry-plane, Springfield is at (0, 9), and Shelbyville is at (0, 9). The cable runs from Centerville to some point (x, 0) on the x-axis where it splits into two branches going to Springfield and 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 answer. To solve this problem we need to minimize the following function of x: f(x): %3D We find that f(x) has a critical number at x = To verify that f(x) has a minimum at this critical number we compute the second derivative f''(x) and find , a positive number. that its value at the critical number is Thus the minimum length of cable needed is Question Help: Message instructor Add Work Submit 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. The idea is to save on the cost of cable by arranging the cable in a Y-shaped configuation. Centerville is located at (12, 0) in the ry-plane, Springfield is at (0, 9), and Shelbyville is at (0, 9). The cable runs from Centerville to some point (x, 0) on the x-axis where it splits into two branches going to Springfield and 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 answer. To solve this problem we need to minimize the following function of x: f(x): %3D We find that f(x) has a critical number at x = To verify that f(x) has a minimum at this critical number we compute the second derivative f''(x) and find , a positive number. that its value at the critical number is Thus the minimum length of cable needed is Question Help: Message instructor Add Work Submit Question

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.7: Solving Systems Of Linear And Quadratic Equations
Problem 14PPS
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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. The idea is to save on the cost of cable by arranging the cable in a Y-shaped configuation. Centerville is located at (12, 0) in the ry-plane, Springfield is at (0, 9), and Shelbyville is at (0, 9). The cable runs from Centerville to some point (x, 0) on the x-axis where it splits into two branches going to Springfield and 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 answer. To solve this problem we need to minimize the following function of x: f(x): %3D We find that f(x) has a critical number at x = To verify that f(x) has a minimum at this critical number we compute the second derivative f''(x) and find , a positive number. that its value at the critical number is Thus the minimum length of cable needed is Question Help: Message instructor Add Work Submit Question
Transcribed Image Text: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. The idea is to save on the cost of cable by arranging the cable in a Y-shaped configuation. Centerville is located at (12, 0) in the ry-plane, Springfield is at (0, 9), and Shelbyville is at (0, 9). The cable runs from Centerville to some point (x, 0) on the x-axis where it splits into two branches going to Springfield and 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 answer. To solve this problem we need to minimize the following function of x: f(x): %3D We find that f(x) has a critical number at x = To verify that f(x) has a minimum at this critical number we compute the second derivative f''(x) and find , a positive number. that its value at the critical number is Thus the minimum length of cable needed is Question Help: Message instructor Add Work Submit Question
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