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\includegraphics[max width=\textwidth, alt={}, center]{76371b0f-0145-4cc4-a147-27bcd749816a-3_451_933_1777_605}
The diagram shows the curve \(y = x ^ { 2 } \mathrm { e } ^ { - x }\).
- Show that the area of the shaded region bounded by the curve, the \(x\)-axis and the line \(x = 3\) is equal to \(2 - \frac { 17 } { \mathrm { e } ^ { 3 } }\).
- Find the \(x\)-coordinate of the maximum point \(M\) on the curve.
- Find the \(x\)-coordinate of the point \(P\) at which the tangent to the curve passes through the origin.