CAIE FP1 2011 November — Question 5

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2011
SessionNovember
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicImplicit equations and differentiation

5 The point \(P ( 2,1 )\) lies on the curve with equation $$x ^ { 3 } - 2 y ^ { 3 } = 3 x y$$ Find
  1. the value of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) at \(P\),
  2. the value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) at \(P\).

5 The point $P ( 2,1 )$ lies on the curve with equation

$$x ^ { 3 } - 2 y ^ { 3 } = 3 x y$$

Find\\
(i) the value of $\frac { \mathrm { d } y } { \mathrm {~d} x }$ at $P$,\\
(ii) the value of $\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }$ at $P$.

\hfill \mbox{\textit{CAIE FP1 2011 Q5}}