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\includegraphics[max width=\textwidth, alt={}, center]{00a4be37-c095-4d9c-a1cd-d03b8ab1d411-2_455_643_1327_694}
The diagram shows the curve \(y = \mathrm { e } ^ { 3 x } - 6 \mathrm { e } ^ { 2 x } + 32\).
- Find the exact \(x\)-coordinate of the minimum point and verify that the \(y\)-coordinate of the minimum point is 0 .
- Find the exact area of the region (shaded in the diagram) enclosed by the curve and the axes.