Help with some calc work?

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 the first stack (closest to New York City), is given by


S=84/x2 + 12/(20-x)2





Note that 84 is 7 times 12. Find the point on the line joining the stacks where the concentration of the deposit is a minimum





and the other question is...


A landscape architect plans to enclose a 2300 square foot rectangular region in a botanical garden. She will use shrubs costing 21 dollars per foot along three sides and fencing costing 12 dollars per foot along the fourth side. The goal is to find the minimum total cost. First express the cost c(x) in terms of x, the length of the side with fencing.


c(x) =


Next give the minimum value of the cost function c(x)

Help with some calc work?
1. Take derivative and set to zero.


-168/x^3+24/(20-x)^3=0


x=13.134





2. xy=2300


Cost = 12x+21x+21*2*y


=12x+21x+21*2*(2300/x)


=33x+96600/x


Minimize, so take derivative...


33-96600/x^2=0


33x^2=96600


x=54.10 feet


So y=42.51 feet

safety boots