Posted by Callie on .
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!

Calculus 1, Help! 
bobpursley,
take drate/dx= 2x ln(1/x)+x=0
solve for x
ln(1/x)=1/2
1/x=sqrte
x= 1/sqrte 
Calculus 1, Help! 
Callie,
isn't the derivative of the rate x*2ln(1/x)1??

Calculus 1, Help! 
Callie,
nevermind, it doesn't change the answer. thankyou very much!