CAIE P1 2011 June — Question 9

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2011
SessionJune
TopicChain Rule

9 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 } { \sqrt { } x } - 1\) and \(P ( 9,5 )\) is a point on the curve.
  1. Find the equation of the curve.
  2. Find the coordinates of the stationary point on the curve.
  3. Find an expression for \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) and determine the nature of the stationary point.
  4. The normal to the curve at \(P\) makes an angle of \(\tan ^ { - 1 } k\) with the positive \(x\)-axis. Find the value of \(k\).