2024 IGCSE Additional Mathematics October/November 0606/11 Q8

8 marks

Given that \(\mathrm{f}''(x)=(3x+5)^{-\frac23}\), \(\mathrm{f}'(1)=6\), and \(\mathrm{f}(1)=20\), find an expression for \(\mathrm{f}(x)\).[8]

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Answer:\(\mathrm{f}(x)=\dfrac14(3x+5)^{\frac43}+4x+12\).

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