- In this question you must show all stages of your working.
\section*{Solutions relying on calculator technology are not acceptable.}
A curve has equation
$$16 x ^ { 3 } - 9 k x ^ { 2 } y + 8 y ^ { 3 } = 875$$
where \(k\) is a constant.
- Show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 6 k x y - 16 x ^ { 2 } } { 8 y ^ { 2 } - 3 k x ^ { 2 } }$$
Given that the curve has a turning point at \(x = \frac { 5 } { 2 }\)
- find the value of \(k\)