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\includegraphics[max width=\textwidth, alt={}, center]{f5be66c3-7234-4039-9b66-199b35430c7d-3_543_850_778_644} The diagram shows the curve \(y = ( 4 - x ) \mathrm { e } ^ { x }\) and its maximum point \(M\). The curve cuts the \(x\)-axis at \(A\) and the \(y\)-axis at \(B\).

1. Write down the coordinates of \(A\) and \(B\).
2. Find the \(x\)-coordinate of \(M\).
3. The point \(P\) on the curve has \(x\)-coordinate \(p\). The tangent to the curve at \(P\) passes through the origin \(O\). Calculate the value of \(p\).