OCR C1 2011 June — Question 10

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Year2011
SessionJune
TopicCurve Sketching
TypeTangent and normal to curve

10 A curve has equation \(y = ( 2 x - 1 ) ( x + 3 ) ( x - 1 )\).
  1. Sketch the curve, indicating the coordinates of all points of intersection with the axes.
  2. Show that the gradient of the curve at the point \(P ( 1,0 )\) is 4 .
  3. The line \(l\) is parallel to the tangent to the curve at the point \(P\). The curve meets \(l\) at the point where \(x = - 2\). Find the equation of \(l\), giving your answer in the form \(y = m x + c\).
  4. Determine whether \(l\) is a tangent to the curve at the point where \(x = - 2\).