A test track for autonomous electric vehicles (EVs) features a banked curve with a certain radius, designed to test the vehicles' ability to navigate turns at a specified speed without depending on friction. This allows for testing under various environmental conditions, which can alter the coefficient of static friction between the tires and the road surface. Determine the minimum and maximum speeds, $v_{\min }$ and $v_{\max }$, at which an autonomous EV can safely handle the banked curve. These speeds should be calculated as functions of the coefficient of static friction (${\mu }_s$), the intended test speed ($v_0$), and the curve's radius ($R$).

$v_{\min }=v_0\sqrt{\frac{1-{\mu }_s\frac{Rg}{v_0^2}}{1+{\mu }_s\frac{v_0^2}{Rg}}}$, $v_{\max }=v_0\sqrt{\frac{1+{\mu }_s\frac{Rg}{v_0^2}}{1-{\mu }_s\frac{v_0^2}{Rg}}}$

$v_{\min }=v_0\sqrt{\frac{1}{1+{\mu }_s\frac{v_0^2}{Rg}}}$, $v_{\max }=v_0\sqrt{\frac{{\mu }_s+\frac{Rg}{v_0^2}}{1-\frac{v_0^2}{Rg}}}$

$v_{\min }=v_0\sqrt{\frac{{\mu }_s-\frac{Rg}{v_0^2}}{1+{\mu }_s}}$, $v_{\max }=v_0\sqrt{\frac{1+{\mu }_s}{{\mu }_s-\frac{v_0^2}{Rg}}}$

$v_{\min }=v_0\sqrt{\frac{1-{\mu }_s\frac{v_0^2}{Rg}}{1+{\mu }_s\frac{Rg}{v_0^2}}}$, $v_{\max }=v_0\sqrt{\frac{1+{\mu }_s\frac{v_0^2}{Rg}}{1-{\mu }_s\frac{Rg}{v_0^2}}}$