CAIE P1 2016 June — Question 3

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2016
SessionJune
TopicStandard Integrals and Reverse Chain Rule

3 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 6 x ^ { 2 } + \frac { k } { x ^ { 3 } }\) and passes through the point \(P ( 1,9 )\). The gradient of the curve at \(P\) is 2 .
  1. Find the value of the constant \(k\).
  2. Find the equation of the curve.