7 A curve \(C\) in the \(x - y\) plane has the property that the gradient of the tangent at the point \(P ( x , y )\) is three times the gradient of the line joining the point \(( 3,2 )\) to \(P\).
- Express this property in the form of a differential equation.
It is given that \(C\) passes through the point \(( 4,3 )\) and that \(x > 3\) and \(y > 2\) at all points on \(C\).
- Determine the equation of \(C\) giving your answer in the form \(y = \mathrm { f } ( x )\).
The curve \(C\) may be obtained by a transformation of part of the curve \(y = x ^ { 3 }\).
- Describe fully this transformation.