CAIE P3 2020 November — Question 10

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2020
SessionNovember
TopicProduct & Quotient Rules

10
\includegraphics[max width=\textwidth, alt={}, center]{5f80ae11-34c3-4d2f-89f8-71b4ac021c7d-16_426_908_262_616} The diagram shows the curve \(y = ( 2 - x ) \mathrm { e } ^ { - \frac { 1 } { 2 } x }\), 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. Give your answer in terms of e.