A curve has the equation $y=\frac{x-4}{3x2}.$

$($i$)$ Find an expression for $\frac{dy}{dx}$ and explain why the curve has no turning points.$($ii$)$ Determine the value of x where the tangent to the curve is a vertical line.$($iii$)$ Find the gradient of the curve when $y=0.$

$[2]$

$($iv$)$ Given that $y$ is increasing at the rate of $0\mathrm{.}28$ units per second at the instant when $x=2,$ find the rate of change of $x$ at this instant.