CAIE P1 2015 June — Question 8

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2015
SessionJune
TopicProduct & Quotient Rules

8 The function f is defined by \(\mathrm { f } ( x ) = \frac { 1 } { x + 1 } + \frac { 1 } { ( x + 1 ) ^ { 2 } }\) for \(x > - 1\).
  1. Find \(\mathrm { f } ^ { \prime } ( x )\).
  2. State, with a reason, whether f is an increasing function, a decreasing function or neither. The function g is defined by \(\mathrm { g } ( x ) = \frac { 1 } { x + 1 } + \frac { 1 } { ( x + 1 ) ^ { 2 } }\) for \(x < - 1\).
  3. Find the coordinates of the stationary point on the curve \(y = \mathrm { g } ( x )\).