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!
No idea where to even start! Any help at all is appreciated! Thanks so much!
Answers
bobpursley
take drate/dx= 2x ln(1/x)+x=0
solve for x
ln(1/x)=1/2
1/x=sqrte
x= 1/sqrte
solve for x
ln(1/x)=1/2
1/x=sqrte
x= 1/sqrte
Callie
isn't the derivative of the rate x*2ln(1/x)-1??
Callie
nevermind, it doesn't change the answer. thankyou very much!