10. The curve \(C\) has the equation \(y = \mathrm { f } ( x )\).
Given that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = 3 - \frac { 2 } { x ^ { 2 } } , \quad x \neq 0 ,$$
and that the point \(A\) on \(C\) has coordinates (2, 6),
- find an equation for \(C\),
- find an equation for the tangent to \(C\) at \(A\), giving your answer in the form \(a x + b y + c = 0\) where \(a , b\) and \(c\) are integers,
- show that the line \(y = x + 3\) is also a tangent to \(C\).