7. (a) Sketch the curve with equation $$y = \frac { k } { x } \quad x \neq 0$$ where \(k\) is a positive constant.
(b) Hence or otherwise, solve $$\frac { 16 } { x } \leqslant 2$$ [BLANK PAGE] \section*{8. In this question you must show detailed reasoning.} The curve \(C _ { 1 }\) has equation \(y = 8 - 10 x + 6 x ^ { 2 } - x ^ { 3 }\)
The curve \(C _ { 2 }\) has equation \(y = x ^ { 2 } - 12 x + 14\)
(a) Verify that when \(x = 1\) the curves \(C _ { 1 }\) and \(C _ { 2 }\) intersect. The curves also intersect when \(x = k\).
Given that \(k < 0\)
(b) use algebra to find the exact value of \(k\).
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