<p>A curve is such that&nbsp;\(\frac{\mathrm{d}^2 y}{\mathrm{d}x^2} = \frac{12}{(3 - 2x)^2}\). 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&nbsp;\(a \ln \left( \frac{b}{c} \right)\) where&nbsp;\(a\), \(b\) and \(c\) are constants.<span class="inline-marks">[8]</span></p>

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.

2025 CGSS PRELIMS P2 Q4

2025 CGSS PRELIMS P2 Q4