$11.(5$ e$.$c$.$ points$)$

A round underwater transmission cable consists of a core of copper wires surrounded by nonconducting insulation. If $\backslash ($ x $\backslash )$ denotes the ratio of the radius of the core to the thickness of the insulation, it is known that the speed of the transmission signal is given by the equation

$\backslash [$

v$=$x$^\{2\}\backslash$ln $\backslash$left$(\backslash$frac$\{1\}\{$x$\}\backslash$right$)$

$\backslash ]$

If the radius of the core is $1$ cm $,$ what insulation thickness $\backslash ($ h $\backslash )$ will allow the greatest transmission speed?