Edexcel C1 2016 June — Question 11

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Year2016
SessionJune
TopicDifferentiation Applications
TypeFind derivative of polynomial

11. The curve \(C\) has equation \(y = 2 x ^ { 3 } + k x ^ { 2 } + 5 x + 6\), where \(k\) is a constant.
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) The point \(P\), where \(x = - 2\), lies on \(C\). The tangent to \(C\) at the point \(P\) is parallel to the line with equation \(2 y - 17 x - 1 = 0\)
    Find
  2. the value of \(k\),
  3. the value of the \(y\) coordinate of \(P\),
  4. the equation of the tangent to \(C\) at \(P\), giving your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers.