CAIE FP1 2018 June — Question 1

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2018
SessionJune
TopicDifferential equations

1 The variables \(x\) and \(y\) are such that \(y = - 1\) when \(x = 0\) and $$\left( x + \frac { \mathrm { d } y } { \mathrm {~d} x } \right) ^ { 3 } = y ^ { 2 } + x$$
  1. Find the value of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) when \(x = 0\).
  2. Find also the value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) when \(x = 0\).