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\includegraphics[max width=\textwidth, alt={}, center]{c5ec981d-7ff7-4698-82c4-eb0506b635a3-2_515_1031_1384_555}
The diagram shows the curve \(y = \mathrm { e } ^ { - x } - \mathrm { e } ^ { - 2 x }\) and its maximum point \(M\). The \(x\)-coordinate of \(M\) is denoted by \(p\).
- Find the exact value of \(p\).
- Show that the area of the shaded region bounded by the curve, the \(x\)-axis and the line \(x = p\) is equal to \(\frac { 1 } { 8 }\).