Variables \(x\) and \(y\) are related by the equation \(y=x\sqrt{1+2x}\).
Find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\).[3]
It is given that when \(y=12\), \(x=4\). Find the approximate change in \(x\) when \(y\) increases from \(12\) by the small amount \(0.06\).[3]
Find the \(x\)-coordinate of the stationary point on the curve \(y=x\sqrt{1+2x}\).[2]