AQA AS Paper 2 2019 June — Question 8

Exam BoardAQA
ModuleAS Paper 2 (AS Paper 2)
Year2019
SessionJune
TopicDifferentiation Applications
TypeFind normal line equation

8 A curve has equation $$y = x ^ { 3 } + p x ^ { 2 } + q x - 45$$ The curve passes through point \(R ( 2,3 )\)
The gradient of the curve at \(R\) is 8
8
  1. Find the value of \(p\) and the value of \(q\).
    8
  2. Calculate the area enclosed between the normal to the curve at \(R\) and the coordinate 8
  3. axes.
    \(9 \quad\) A curve \(C\) has equation \(y = \mathrm { f } ( x )\) where $$f ( x ) = ( x - 2 ) ( x - 3 ) ^ { 2 }$$