Posted by **Callie** on Wednesday, August 17, 2011 at 9:50pm.

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**, Wednesday, August 17, 2011 at 9:54pm
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**, Wednesday, August 17, 2011 at 10:04pm
isn't the derivative of the rate x*2ln(1/x)-1??

- Calculus 1, Help! -
**Callie**, Wednesday, August 17, 2011 at 10:08pm
nevermind, it doesn't change the answer. thankyou very much!

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