The curve $y = \mathrm{f}(x)$ is such that $\mathrm{f}''(x) = 2e^x + e^{-2x}$. The $y$-ax

Question

The curve $y = \mathrm{f}(x)$ is such that $\mathrm{f}''(x) = 2e^x + e^{-2x}$. The $y$-axis is a normal to the curve at the point $Q$, where $y = 1$. Show that $Q$ is a stationary point.[2] Hence, find an expression for $\mathrm{f}(x)$.[6]

Accepted Answer

(a) $Q$ is a stationary point. (b) $\displaystyle \mathrm{f}(x)=2e^x+\frac{1}{4}e^{-2x}-\frac{3}{2}x-\frac{5}{4}$.

2025 AHS PRELIMS P2 Q6

2025 AHS PRELIMS P2 Q6

Video Solution:

Solution:

Solution locked