Show that the gradient of the curve \(y=x(x-3)^2\) is zero at the point \(P(1,4)\), and sketch the curve.

The tangent at \(P\) cuts the curve again at \(Q\). Calculate the area between the chord \(PQ\) and the curve.

Show that the gradient of the curve \(y=x(x-3)^2\) is zero at the point \(P(1,4)\), and sketch the curve.

The tangent at \(P\) cuts the curve again at \(Q\). Calculate the area between the chord \(PQ\) and the curve.