Chapter 4.3, Problem 35E

A smokestack deposits soot on the ground with a concentration inversely proportional to the square of the distance from the stack. With two smokestacks 20miles apart, the concentration of the combined deposits on the line joining them, at a distance x from one stack, is given by

$S=\frac{k_1}{x^2}+\frac{k^2}{{(20-x)}^2}$

where k₁ and k₂ are positive constants which depend on the quantity of smoke each stack is emitting. If k₁ = 7k₂, find the point on the line joining the stacks where the concentration of the deposit is a minimum.