CAIE P1 2019 November — Question 8

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2019
SessionNovember
TopicIntegration by Substitution

8 A function f is defined for \(x > \frac { 1 } { 2 }\) and is such that \(\mathrm { f } ^ { \prime } ( x ) = 3 ( 2 x - 1 ) ^ { \frac { 1 } { 2 } } - 6\).
  1. Find the set of values of \(x\) for which f is decreasing.
  2. It is now given that \(\mathrm { f } ( 1 ) = - 3\). Find \(\mathrm { f } ( x )\).