7 A curve is defined, for \(x > 0\), by the equation \(y = \mathrm { f } ( x )\), where
$$\mathrm { f } ( x ) = \frac { x ^ { 8 } - 1 } { x ^ { 3 } }$$
- Express \(\frac { x ^ { 8 } - 1 } { x ^ { 3 } }\) in the form \(x ^ { p } - x ^ { q }\), where \(p\) and \(q\) are integers.
- Hence differentiate \(\mathrm { f } ( x )\) to find \(\mathrm { f } ^ { \prime } ( x )\).
- Hence show that f is an increasing function.
- Find the gradient of the normal to the curve at the point \(( 1,0 )\).