A curve $C$ has equation $2{{y}^{3}}-{{y}^{2}}=x{{\mathrm{e}}^{x}}$. Find the equations of the t

Question

A curve $C$ has equation $2{{y}^{3}}-{{y}^{2}}=x{{\mathrm{e}}^{x}}$. Find the equations of the tangents which are parallel to the $y$-axis.[5] It is given that the tangents found in part (a) make an acute angle of $\frac{\pi }{6}$ radians with the line $y=mx+1$. Find the values of $m$.[2]

Accepted Answer

(a) Tangents $x=-4.88$, $x=-0.0385$, and $x=0$ (3 s.f. where appropriate) (b) $m=\pm\sqrt3$

2024 HCI P2 Q3

2024 HCI P2 Q3

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