- The curve \(C\) has equation \(y = \mathrm { f } ( x )\) where
$$f ( x ) = 2 x ^ { 3 } - k x ^ { 2 } + 14 x + 24$$
and \(k\) is a constant.
- Find, in simplest form,
- \(\mathrm { f } ^ { \prime } ( x )\)
- \(\mathrm { f } ^ { \prime \prime } ( x )\)
The curve with equation \(y = \mathrm { f } ^ { \prime } ( x )\) intersects the curve with equation \(y = \mathrm { f } ^ { \prime \prime } ( x )\) at the points \(A\) and \(B\).
Given that the \(x\) coordinate of \(A\) is 5
- find the value of \(k\).
- Hence find the coordinates of \(B\).