Edexcel C1 2007 June — Question 9

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Year2007
SessionJune
TopicCurve Sketching
TypeCurve from derivative information

9. The curve \(C\) with equation \(y = \mathrm { f } ( x )\) passes through the point \(( 5,65 )\). Given that \(\mathrm { f } ^ { \prime } ( x ) = 6 x ^ { 2 } - 10 x - 12\),
  1. use integration to find \(\mathrm { f } ( x )\).
  2. Hence show that \(\mathrm { f } ( x ) = x ( 2 x + 3 ) ( x - 4 )\).
  3. In the space provided on page 17, sketch \(C\), showing the coordinates of the points where \(C\) crosses the \(x\)-axis. \includegraphics[max width=\textwidth, alt={}, center]{c0db3fe8-62ec-41e3-acaf-66b2c7b2754d-11_76_40_2646_1894}