CAIE P1 2017 June — Question 9

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2017
SessionJune
TopicChain Rule

9 The equation of a curve is \(y = 8 \sqrt { } x - 2 x\).
  1. Find the coordinates of the stationary point of the curve.
  2. Find an expression for \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) and hence, or otherwise, determine the nature of the stationary point.
  3. Find the values of \(x\) at which the line \(y = 6\) meets the curve.
  4. State the set of values of \(k\) for which the line \(y = k\) does not meet the curve.