3
\includegraphics[max width=\textwidth, alt={}, center]{76df3465-9617-4f2b-a8b7-f474b2817504-04_776_483_310_769} The diagram shows the curve with equation \(y = 8 \mathrm { e } ^ { - x } - \mathrm { e } ^ { 2 x }\). The curve crosses the \(y\)-axis at the point \(A\) and the \(x\)-axis at the point \(B\). The shaded region is bounded by the curve and the two axes.

1. Find the gradient of the curve at \(A\).
   \includegraphics[max width=\textwidth, alt={}, center]{76df3465-9617-4f2b-a8b7-f474b2817504-04_2715_35_141_2011}
2. Show that the \(x\)-coordinate of \(B\) is \(\ln 2\) and hence find the area of the shaded region.