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\includegraphics[max width=\textwidth, alt={}, center]{84df6b9a-6118-44a2-9c18-512039ded4fd-3_416_677_258_733}
The diagram shows part of the curve \(y = \left( 2 x - x ^ { 2 } \right) \mathrm { e } ^ { \frac { 1 } { 2 } x }\) and its maximum point \(M\).
- Find the exact \(x\)-coordinate of \(M\).
- Find the exact value of the area of the shaded region bounded by the curve and the positive \(x\)-axis.