<p>The curve \(C\) has equation \(y = \frac{1}{4x - x^2}\).</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find \(\frac{\mathrm{d}y}{\mathrm{d}x}\). Hence, find the \(x\)-coordinate, \(x = x_1\), of the turning point on \(C\) and determine its nature.</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Using calculus, find the exact area of the region between \(C\), the \(x\)-axis and the lines with equations \(x = 1\) and \(x = x_1\).</span><span class="inline-marks">[3]</span></div></li></ol>

The curve \(C\) has equation \(y = \frac{1}{4x - x^2}\).

Find \(\frac{\mathrm{d}y}{\mathrm{d}x}\). Hence, find the \(x\)-coordinate, \(x = x_1\), of the turning point on \(C\) and determine its nature.

Using calculus, find the exact area of the region between \(C\), the \(x\)-axis and the lines with equations \(x = 1\) and \(x = x_1\).

2025 JPJC P1 Q1

2025 JPJC P1 Q1