Question:

In a submarine telegraph cable, the speed of signaling varies as x2log(1/x) x^2 \log(1/x) , where x x is the ratio of the radius of the core to that of the covering. To attain the greatest speed, the value of this ratio is:

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When optimizing physical systems, use calculus to find critical points where derivatives equal zero.
Updated On: Mar 17, 2025
  • 12 \frac{1}{2}
  • 23 \frac{2}{3}
  • 3e \frac{3}{\sqrt{e}}
  • 1e \frac{1}{\sqrt{e}}
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The Correct Option is D

Solution and Explanation

To maximize the speed, we take the derivative of the function S(x) S(x) with respect to x x and set it to zero. This results in the optimal ratio of x=1e x = \frac{1}{\sqrt{e}} .

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