In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. A curve has equation $$\[ 16 x^{3}-9 k x^{2} y+8 y^{3}=875 \]$$ where $$\(k\)$$ is a constant. (a) Show that $$\[ \frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{6 k x y-16 x^{2}}{8 y^{2}-3 k x^{2}} \]$$ (4) Given that the curve has a turning point at $$\(x=\frac{5}{2}\)$$ (b) find the value of $$\(k\)$$ (4)

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