| Exam Board | Edexcel |
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| Module | P1 (Pure Mathematics 1) |
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| Year | 2024 |
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| Session | June |
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| Topic | Product & Quotient Rules |
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- The curve \(C\) has equation \(y = \mathrm { f } ( x )\) where \(x > 0\)
Given that
- \(\mathrm { f } ^ { \prime } ( x ) = 6 x - \frac { ( 2 x - 1 ) ( 3 x + 2 ) } { 2 \sqrt { x } }\)
- the point \(P ( 4,12 )\) lies on \(C\)
- find the equation of the normal to \(C\) at \(P\), giving your answer in the form \(y = m x + c\) where \(m\) and \(c\) are integers to be found,
- find \(\mathrm { f } ( x )\), giving each term in simplest form.