CAIE P2 2010 November — Question 4

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2010
SessionNovember
TopicParametric equations

4 The parametric equations of a curve are $$x = 1 + \ln ( t - 2 ) , \quad y = t + \frac { 9 } { t } , \quad \text { for } t > 2$$
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { \left( t ^ { 2 } - 9 \right) ( t - 2 ) } { t ^ { 2 } }\).
  2. Find the coordinates of the only point on the curve at which the gradient is equal to 0 .