| Exam Board | Edexcel |
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| Module | PMT Mocks (PMT Mocks) |
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| Topic | Product & Quotient Rules |
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12. A curve has equation \(y = \frac { 2 x e ^ { x } } { x + k }\) where \(k\) is a positive constant.
i. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { e ^ { x } \left( 2 x ^ { 2 } + 2 k x + 2 k \right) } { ( x + k ) ^ { 2 } }\)
ii. Given that the curve has exactly one stationary point find the value of \(k\).