2026 IGCSE Additional Mathematics May/June 0606/11 Q10

8 marks

A curve has equation \(y=\mathrm{f}(x)\), where \(\mathrm{f}''(x)=(2x+10)^{-1/2}-2x\).

The curve has a stationary point at \(\left(3,\dfrac{64}{3}\right)\).

Find the equation of the curve.[8]

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Answer:\(y=\dfrac13(2x+10)^{3/2}-\dfrac{x^3}{3}+5x-6\)

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