CAIE FP1 2017 June — Question 3

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2017
SessionJune
TopicImplicit equations and differentiation

3 A curve \(C\) has equation \(\tan y = x\), for \(x > 0\).
  1. Use implicit differentiation to show that $$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } = - 2 x \left( \frac { \mathrm {~d} y } { \mathrm {~d} x } \right) ^ { 2 }$$
  2. Hence find the value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) at the point \(\left( 1 , \frac { 1 } { 4 } \pi \right)\) on \(C\).