10. The curve \(C\) has equation
$$y = a x ^ { 3 } - 3 x ^ { 2 } + 3 x + b$$
where \(a\) and \(b\) are constants.
Given that
- the point \(( 2,5 )\) lies on \(C\)
- the gradient of the curve at \(( 2,5 )\) is 7
- find the value of \(a\) and the value of \(b\).
- Prove that \(C\) has no turning points.