5 In this question you must show detailed reasoning.
- Show that the gradient of the curve \(\mathrm { y } = \sqrt { \mathrm { x } } \left( \frac { 1 } { \mathrm { x } ^ { 2 } } - 2 \mathrm { x } \right)\) at the point \(\left( \frac { 1 } { 4 } , \frac { 31 } { 4 } \right)\) is \(- \frac { 99 } { 2 }\).
- Find the equation of the tangent to the curve at \(\left( \frac { 1 } { 4 } , \frac { 31 } { 4 } \right)\) giving your answer in the form \(\mathrm { ax } + \mathrm { by } + \mathrm { c } = 0\), where \(a , b\) and \(c\) are integers.