It is given that $y=\mathrm{f}\left( x \right)$, where ${{y}^{3}}+8=3xy$. Find the Mac

Question

It is given that $y=\mathrm{f}\left( x \right)$, where ${{y}^{3}}+8=3xy$. Find the Maclaurin series for $\mathrm{f}\left( x \right)$ up to and including the term in ${{x}^{3}}$.[6] Hence write down the equation of the normal at the point on the curve of $y=\mathrm{f}\left( x \right)$ at $x=0$.[1]

Accepted Answer

$y=-2-\frac{1}{2}x+\frac{1}{96}{{x}^{3}}$. Hence, the equation of the normal to the curve at $x=0$ is $y=-2+2x$

2024 DHS P2 Q2

2024 DHS P2 Q2

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