- In this question you must show detailed reasoning.
\section*{Solutions relying on calculator technology are not acceptable.}
The curve \(C _ { 1 }\) has equation \(y = 8 - 10 x + 6 x ^ { 2 } - x ^ { 3 }\)
The curve \(C _ { 2 }\) has equation \(y = x ^ { 2 } - 12 x + 14\)
- Verify that when \(x = 1\) the curves \(C _ { 1 }\) and \(C _ { 2 }\) intersect.
The curves also intersect when \(x = k\).
Given that \(k < 0\) - use algebra to find the exact value of \(k\).