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Calculus / Calculus: Single Variable 6 / Chapter 4.3 / Problem 33

Calculus: Single Variable | 6th Edition | ISBN: 9780470888643 | Authors: Deborah Hughes-Hallett, Andrew M. Gleason, William G. McCallum, Daniel E. Flath, Patti Frazer Lock, David O. Lomen, David Lovelock, & 9 more

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A smokestack deposits soot on the ground with a concentration inversely proportional to

Chapter 4, Problem 33

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QUESTION:

A smokestack deposits soot on the ground with a concentration inversely proportional to the square of the distance from the stack. With two smokestacks 20 miles apart, the concentration of the combined deposits on the line joining them, at a distance x from one stack, is given by where and are positive constants which depend on the quantity of smoke each stack is emitting. If , find the point on the line joining the stacks where the concentration of the deposit is a minimum.

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QUESTION:

A smokestack deposits soot on the ground with a concentration inversely proportional to the square of the distance from the stack. With two smokestacks 20 miles apart, the concentration of the combined deposits on the line joining them, at a distance x from one stack, is given by where and are positive constants which depend on the quantity of smoke each stack is emitting. If , find the point on the line joining the stacks where the concentration of the deposit is a minimum.

ANSWER:

Step 1 of 4

Given ,

Let and

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