CAIE P1 2022 November — Question 7

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2022
SessionNovember
TopicStandard Integrals and Reverse Chain Rule

7 The curve \(y = \mathrm { f } ( x )\) is such that \(\mathrm { f } ^ { \prime } ( x ) = \frac { - 3 } { ( x + 2 ) ^ { 4 } }\).
  1. The tangent at a point on the curve where \(x = a\) has gradient \(- \frac { 16 } { 27 }\). Find the possible values of \(a\).
  2. Find \(\mathrm { f } ( x )\) given that the curve passes through the point \(( - 1,5 )\).