CAIE P3 2022 November — Question 9

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2022
SessionNovember
TopicProduct & Quotient Rules

9
\includegraphics[max width=\textwidth, alt={}, center]{98001cfe-46a1-4c8f-9230-c140ebff6176-14_535_1082_274_520} The diagram shows part of the curve \(y = ( 3 - x ) \mathrm { e } ^ { - \frac { 1 } { 3 } x }\) for \(x \geqslant 0\), and its minimum point \(M\).
  1. Find the exact coordinates of \(M\).
  2. Find the area of the shaded region bounded by the curve and the axes, giving your answer in terms of e.