The curve $C$ has equation $$y = x(x+1)(x-2)^4.$$ Determine the coordinates of all the stationary points of $C$ and the nature of each.

Sketch $C$.

In separate diagrams draw sketches of the curves whose equations are:

1. $y^2 = x(x+1)(x-2)^4$
2. $y = x^2(x^2+1)(x^2-2)^4$