CAIE P1 2005 June — Question 10

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2005
SessionJune
TopicInequalities

10 The equation of a curve is \(y = x ^ { 2 } - 3 x + 4\).
  1. Show that the whole of the curve lies above the \(x\)-axis.
  2. Find the set of values of \(x\) for which \(x ^ { 2 } - 3 x + 4\) is a decreasing function of \(x\). The equation of a line is \(y + 2 x = k\), where \(k\) is a constant.
  3. In the case where \(k = 6\), find the coordinates of the points of intersection of the line and the curve.
  4. Find the value of \(k\) for which the line is a tangent to the curve.