CAIE P1 2024 June — Question 9

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2024
SessionJune
TopicProduct & Quotient Rules

9 A function f is such that \(\mathrm { f } ^ { \prime } ( x ) = 6 ( 2 x - 3 ) ^ { 2 } - 6 x\) for \(x \in \mathbb { R }\).
  1. Determine the set of values of \(x\) for which \(\mathrm { f } ( x )\) is decreasing.
  2. Given that \(\mathrm { f } ( 1 ) = - 1\), find \(\mathrm { f } ( x )\).