3 The curve \(C\) has equation
$$x y ^ { 3 } - 4 x ^ { 3 } y = 3$$
- Show that, at the point \(( - 1,1 )\) on \(C , \frac { \mathrm { dy } } { \mathrm { dx } } = 11\).
- Find the value of \(\frac { d ^ { 2 } y } { d x ^ { 2 } }\) at the point \(( - 1,1 )\).
\includegraphics[max width=\textwidth, alt={}, center]{59982339-c496-4bd7-8dcd-9b257f3afc02-06_535_1584_276_276}
The diagram shows the curve with equation \(\mathrm { y } = \frac { \ln \mathrm { x } } { \mathrm { x } ^ { 2 } }\) for \(x \geqslant 2\), together with a set of \(( N - 2 )\) rectangles
of unit width.