(a) Given that

\(y=x\sqrt{x+2},\)

show that

\(\frac{dy}{dx}=\frac{Ax+B}{2\sqrt{x+2}},\)

where \(A\) and \(B\) are constants.

(b) Find the exact coordinates of the stationary point of the curve \(y=x\sqrt{x+2}\).

(c) Determine the nature of this stationary point.