The diagram shows the curve \(y = x^2 e^{-x}\).

(i) Show that the area of the shaded region bounded by the curve, the \(x\)-axis and the line \(x = 3\) is equal to \(2 - \frac{17}{e^3}\).

(ii) Find the \(x\)-coordinate of the maximum point \(M\) on the curve.

(iii) Find the \(x\)-coordinate of the point \(P\) at which the tangent to the curve passes through the origin.