Question

The rate of transmission r in a telephone cable is obseed to be approximately r(x)=x^2*ln(1/x, where x is the ratio of the radius of the core to the thickness of the insulation. Due to manufacturing constraints, the only possible ratios are 1/4<=x<=1. What value of x gves the maximum rate of transmission?

No idea where to even start! Any help at all is appreciated! Thanks so much!

Answer 1

take drate/dx= 2x ln(1/x)+x=0
solve for x

ln(1/x)=1/2
1/x=sqrte
x= 1/sqrte

Answer 2

isn't the derivative of the rate x*2ln(1/x)-1??

Answer 3

nevermind, it doesn't change the answer. thankyou very much!