A curve is such that $\frac{\mathrm{d}^2 y}{\mathrm{d}x^2} = \frac{12}{(3 - 2x)^2}$. Given th

Question

A curve is such that $\frac{\mathrm{d}^2 y}{\mathrm{d}x^2} = \frac{12}{(3 - 2x)^2}$. Given that the curve passes through the points $\left( \frac{1}{2}, 1 \right)$ and $(1, \ln(8e^2))$, show that the $y$-intercept of the curve can be expressed as $a \ln \left( \frac{b}{c} \right)$ where $a$, $b$ and $c$ are constants.[8]

Accepted Answer

$y\text{-intercept}=3\ln\left(\frac{2}{3}\right)$, so $a=3$, $b=2$, and $c=3$.

2025 CGSS PRELIMS P2 Q4

2025 CGSS PRELIMS P2 Q4

Solution:

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