Edexcel C1 2014 January — Question 10

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Year2014
SessionJanuary
TopicDifferentiation Applications
TypeTangent parallel to given line

10. The curve \(C\) has equation \(y = x ^ { 3 } - 2 x ^ { 2 } - x + 3\) The point \(P\), which lies on \(C\), has coordinates \(( 2,1 )\).
  1. Show that an equation of the tangent to \(C\) at the point \(P\) is \(y = 3 x - 5\) The point \(Q\) also lies on \(C\).
    Given that the tangent to \(C\) at \(Q\) is parallel to the tangent to \(C\) at \(P\),
  2. find the coordinates of the point \(Q\).