Edexcel C3 2007 June — Question 3

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
Year2007
SessionJune
TopicProduct & Quotient Rules

3. A curve \(C\) has equation $$y = x ^ { 2 } \mathrm { e } ^ { x }$$
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\), using the product rule for differentiation.
  2. Hence find the coordinates of the turning points of \(C\).
  3. Find \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
  4. Determine the nature of each turning point of the curve \(C\).