7. The curve \(C\) has equation \(y = 4 x ^ { 2 } + \frac { 5 - x } { x } , x \neq 0\). The point \(P\) on \(C\) has \(x\)-coordinate 1 .
- Show that the value of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) at \(P\) is 3 .
- Find an equation of the tangent to \(C\) at \(P\).
This tangent meets the \(x\)-axis at the point \(( k , 0 )\).
- Find the value of \(k\).