Edexcel P4 2022 June — Question 4

Exam BoardEdexcel
ModuleP4 (Pure Mathematics 4)
Year2022
SessionJune
TopicImplicit equations and differentiation

  1. In this question you must show all stages of your working.
\section*{Solutions relying on calculator technology are not acceptable.} A curve has equation $$16 x ^ { 3 } - 9 k x ^ { 2 } y + 8 y ^ { 3 } = 875$$ where \(k\) is a constant.
  1. Show that $$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 6 k x y - 16 x ^ { 2 } } { 8 y ^ { 2 } - 3 k x ^ { 2 } }$$ Given that the curve has a turning point at \(x = \frac { 5 } { 2 }\)
  2. find the value of \(k\)