A curve is such that $\frac{\mathrm{d}^2y}{\mathrm{d}x^2}=3e^{2x}-e^{-x}$. The curve cuts the

Question

A curve is such that $\frac{\mathrm{d}^2y}{\mathrm{d}x^2}=3e^{2x}-e^{-x}$. The curve cuts the y-axis at $P (0,1)$ and has a gradient of $4$ at $P$. Show that the curve has no stationary points.[3] Find the equation of the curve.[4]

Accepted Answer

(a) $\dfrac{\mathrm{d}y}{\mathrm{d}x}>0$ for all real $x$, so there are no stationary points (b) $y=\dfrac{3}{4}e^{2x}-e^{-x}+\dfrac{3}{2}x+\dfrac{5}{4}$

2025 MSHS PRELIMS P1 Q9

2025 MSHS PRELIMS P1 Q9

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