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aight wide. Electric power for the house must come from a power station on the opposite side of the canal, 500 m downstream. If it cost twice as much to lay ca

aight wide. Electric power for the house must come from a power station on the opposite side of the canal, 500 m downstream. If it cost twice as much to lay ca

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section: Chapter Questions
Problem 16T
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Please see attached for my question and the equation I created. I want to know how to find the first derivative to find the critical point and the optimal value of x for minimal cost.

f. An isolated farm house is located on the bank of a straight canal that is 200 m wide. Electric power for the house must come from a power station on the opposite side of the canal, 500 m downstream. If it cost twice as much to lay cable underwater as it does to lay cable on land, what path should be chosen to minimize the cost? f = optimal minimal cost entire function h = hypoteneuse from house to power 500 - x = vertical component along canal of h 200 = horizontal component across canal of h x = cable on land along canal After simplifying: a = cost f= * = ax + (2a (h)) f = ax + (2a (√x² − 1000x + 290 000)
Transcribed Image Text:f. An isolated farm house is located on the bank of a straight canal that is 200 m wide. Electric power for the house must come from a power station on the opposite side of the canal, 500 m downstream. If it cost twice as much to lay cable underwater as it does to lay cable on land, what path should be chosen to minimize the cost? f = optimal minimal cost entire function h = hypoteneuse from house to power 500 - x = vertical component along canal of h 200 = horizontal component across canal of h x = cable on land along canal After simplifying: a = cost f= * = ax + (2a (h)) f = ax + (2a (√x² − 1000x + 290 000)
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