OCR H240/02 — Question 2

Exam BoardOCR
ModuleH240/02 (Pure Mathematics and Statistics)
TopicDifferentiation Applications
TypeFind second derivative

2 A curve has equation \(y = x ^ { 5 } - 5 x ^ { 4 }\).
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) and \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
  2. Verify that the curve has a stationary point when \(x = 4\).
  3. Determine the nature of this stationary point.