\end{figure}
Fig. 12 shows part of the curve \(y = x ^ { 4 }\) and the line \(y = 8 x\), which intersect at the origin and the point P .
(A) Find the coordinates of P , and show that the area of triangle OPQ is 16 square units.
(B) Find the area of the region bounded by the line and the curve.
If \(f ( x ) = x ^ { 3 }\), find \(f ^ { \prime } ( x )\) from first principles.