2025 DHS P2 Q1
2025 DHS P2 Q1
5 marks
A curve \(C\) has equation \(y=x+\frac{9}{x+1}\).
- Using differentiation, find the range of values of \(x\) such that \(C\) concaves upwards.[2]
- Sketch \(C\).[3]
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Answer:(a) \(x>-1\) (b) Asymptotes \(x=-1\) and \(y=x\); maximum \((-4,-7)\), minimum \((2,5)\), and \(y\)-intercept \((0,9)\), with no real \(x\)-intercept
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