| Exam Board | Edexcel |
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| Module | P1 (Pure Mathematics 1) |
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| Year | 2023 |
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| Session | January |
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| Topic | Chain Rule |
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- A curve \(C\) has equation \(y = \mathrm { f } ( x ) , \quad x > 0\)
Given that
- \(\mathrm { f } ^ { \prime \prime } ( x ) = 4 x + \frac { 1 } { \sqrt { x } }\)
- the point \(P\) has \(x\) coordinate 4 and lies on \(C\)
- the tangent to \(C\) at \(P\) has equation \(y = 3 x + 4\)
- find an equation of the normal to \(C\) at \(P\)
- find \(\mathrm { f } ( x )\), writing your answer in simplest form.