10. The curve \(C\) has the equation \(y = \mathrm { f } ( x )\).
Given that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = 8 x - \frac { 2 } { x ^ { 3 } } , \quad x \neq 0$$
and that the point \(P ( 1,1 )\) lies on \(C\),
- find an equation for the tangent to \(C\) at \(P\) in the form \(y = m x + c\),
- find an equation for \(C\),
- find the \(x\)-coordinates of the points where \(C\) meets the \(x\)-axis, giving your answers in the form \(k \sqrt { 2 }\).