2024 IGCSE Additional Mathematics October/November 0606/11 Q9

The equation of a curve is \(y=\dfrac{\mathrm{e}^{-3x+2}}{x+1}\) where \(x<-1\).

1. Show that \(\dfrac{\mathrm{d}y}{\mathrm{d}x}=\dfrac{\mathrm{e}^{-3x+2}}{(x+1)^2}(Ax+B)\) where \(A\) and \(B\) are integers to be found.[5]
2. Hence show that there is only one stationary point on the curve and find its exact coordinates.[3]