The diagram shows the graph of curve $C$ with equation $y{{e}^{-y}}-\frac{1}{2}x=0$ for $y\ge 0$. Th

Question

The diagram shows the graph of curve $C$ with equation $y{{e}^{-y}}-\frac{1}{2}x=0$ for $y\ge 0$. The $y$-axis is an asymptote to $C$. Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $y$. Hence find the equation of the tangent to $C$ which is parallel to the $y-$axis. [4]

Accepted Answer

$x = \frac{2}{e}$

2016 DHS Promo Q7(i)

2016 DHS Promo Q7(i)

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