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Centerville is located at (9, 0) in the æy-plane, Springfield is at (0, 8), and Shelbyville is at (0, – 8). 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 æ: f(x) = We find that f(x) has a critical number at æ = To verify that f(æ) has a minimum at this critical number we compute the second derivative ƒ "(x) and find that its |value at the critical number is Preview Preview Preview , a positive number.

Centerville is located at (9, 0) in the æy-plane, Springfield is at (0, 8), and Shelbyville is at (0, – 8). 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 æ: f(x) = We find that f(x) has a critical number at æ = To verify that f(æ) has a minimum at this critical number we compute the second derivative ƒ "(x) and find that its |value at the critical number is Preview Preview Preview , a positive number.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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Centerville is located at (9, 0) in the æy-plane, Springfield is at (0, 8), and Shelbyville is at (0, – 8). 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 æ: f(x) = We find that f(x) has a critical number at æ = To verify that f(æ) has a minimum at this critical number we compute the second derivative ƒ "(x) and find that its |value at the critical number is Preview Preview Preview , a positive number.
Transcribed Image Text:Centerville is located at (9, 0) in the æy-plane, Springfield is at (0, 8), and Shelbyville is at (0, – 8). 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 æ: f(x) = We find that f(x) has a critical number at æ = To verify that f(æ) has a minimum at this critical number we compute the second derivative ƒ "(x) and find that its |value at the critical number is Preview Preview Preview , a positive number.
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