OCR C1 2009 January — Question 10

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Year2009
SessionJanuary
TopicDifferentiation Applications
TypeFind normal line equation

10 A curve has equation \(y = x ^ { 2 } + x\).
  1. Find the gradient of the curve at the point for which \(x = 2\).
  2. Find the equation of the normal to the curve at the point for which \(x = 2\), giving your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers.
  3. Find the values of \(k\) for which the line \(y = k x - 4\) is a tangent to the curve.