4 The curve sketched below passes through the point \(A ( - 2,0 )\).
\includegraphics[max width=\textwidth, alt={}, center]{889639d6-0a31-4569-8370-1e72291a0c47-3_538_734_365_662} The curve has equation \(y = 14 - x - x ^ { 4 }\) and the point \(P ( 1,12 )\) lies on the curve.

1. 1. Find the gradient of the curve at the point \(P\).
   2. Hence find the equation of the tangent to the curve at the point \(P\), giving your answer in the form \(y = m x + c\).
2. 1. Find \(\int _ { - 2 } ^ { 1 } \left( 14 - x - x ^ { 4 } \right) \mathrm { d } x\).
   2. Hence find the area of the shaded region bounded by the curve \(y = 14 - x - x ^ { 4 }\) and the line \(A P\).
      (2 marks)