The diagram shows the curve $y = {e^{ - x}} - {e^{ - 2x}}$ and its maximum point $M$. The x-coordinate of $M$ is denoted by $p$.
a) Find the exact value of $p$.
b) Show that the area of the shaded region bounded by the curve, the x-axis and the line $x = p$ is equal to $\frac{1}{8}$.

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