CAIE FP1 2015 June — Question 6

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2015
SessionJune
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicImplicit equations and differentiation

6 A curve has equation \(x ^ { 2 } - 6 x y + 25 y ^ { 2 } = 16\). Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 0\) at the point \(( 3,1 )\). By finding the value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) at the point \(( 3,1 )\), determine the nature of this turning point.

6 A curve has equation $x ^ { 2 } - 6 x y + 25 y ^ { 2 } = 16$. Show that $\frac { \mathrm { d } y } { \mathrm {~d} x } = 0$ at the point $( 3,1 )$.

By finding the value of $\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }$ at the point $( 3,1 )$, determine the nature of this turning point.

\hfill \mbox{\textit{CAIE FP1 2015 Q6}}