3.45: Derivative of a composite power and stationary point

Show that $\dfrac{\mathrm{d}y}{\mathrm{d}x} = \dfrac{(5 - x^{3})^{\frac{1}{2}}}{(x^{2} + 1)^{2}}(Ax^{2} + Bx + C)$, where $A$, $B$ and $C$ are integers.

Find the $x$-coordinate of the stationary point on the curve.

Explain how you could determine the nature of this stationary point. (You are not required to find the nature.)