1.42: Product rule and stationary point

Given that $y = (x^{2} - 1)\sqrt{5x + 2}$, show that $\dfrac{\mathrm{d}y}{\mathrm{d}x} = \dfrac{Ax^{2} + Bx + C}{2\sqrt{5x + 2}}$, where $A$, $B$ and $C$ are integers.

Find the coordinates of the stationary point of the curve $y = (x^{2} - 1)\sqrt{5x + 2}$, for $x > 0$. Give each coordinate correct to 2 significant figures.

Determine the nature of this stationary point.