CAIE P3 2012 November — Question 5

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2012
SessionNovember
TopicDifferentiating Transcendental Functions

5 The expression \(\mathrm { f } ( x )\) is defined by \(\mathrm { f } ( x ) = 3 x \mathrm { e } ^ { - 2 x }\).
  1. Find the exact value of \(\mathrm { f } ^ { \prime } \left( - \frac { 1 } { 2 } \right)\).
  2. Find the exact value of \(\int _ { - \frac { 1 } { 2 } } ^ { 0 } \mathrm { f } ( x ) \mathrm { d } x\).