4．Given that \(\mathrm { f } ( x ) = \mathrm { e } ^ { x ^ { 3 } - 2 x }\)
（a）find \(\mathrm { f } ^ { \prime } ( x )\) The curves \(C _ { 1 }\) and \(C _ { 2 }\) are defined by the functions g and h respectively，where $$\begin{array} { l l } \mathrm { g } ( x ) = 8 x ^ { 3 } \mathrm { e } ^ { x ^ { 3 } - 2 x } & x \in \mathbb { R } , x > 0
\mathrm {~h} ( x ) = \left( 3 x ^ { 5 } + 4 x \right) \mathrm { e } ^ { x ^ { 3 } - 2 x } & x \in \mathbb { R } , x > 0 \end{array}$$ （b）Find the \(x\) coordinates of the points of intersection of \(C _ { 1 }\) and \(C _ { 2 }\) Given that \(C _ { 1 }\) lies above \(C _ { 2 }\) between these points of intersection，
（c）find the area of the region bounded by the curves between these two points．
Give your answer in the form \(A + B \mathrm { e } ^ { C }\) where \(A , B\) ，and \(C\) are exact real numbers to be found．