CAIE P2 2002 June — Question 7

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2002
SessionJune
TopicParametric equations

7 The parametric equations of a curve are $$x = t + 2 \ln t , \quad y = 2 t - \ln t$$ where \(t\) takes all positive values.
  1. Express \(\frac { d y } { d x }\) in terms of \(t\).
  2. Find the equation of the tangent to the curve at the point where \(t = 1\).
  3. The curve has one stationary point. Show that the \(y\)-coordinate of this point is \(1 + \ln 2\) and determine whether this point is a maximum or a minimum.