<p>The equation of the curve is \(y = \mathrm{f}(x)\), where&nbsp;\(\mathrm{f}(x) = (x + 4)\sqrt{2x - 3}\), \(x &gt; \frac{3}{2}\).</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Show that&nbsp;\(\mathrm{f}'(x) = \frac{px + q}{\sqrt{2x - 3}}\), where&nbsp;\(p\) and \(q\) are integers.<span class="inline-marks">[3]</span></div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">Find the \(x\)-coordinates of the points where the gradient of the normal is \(-\frac{1}{7}\).<span class="inline-marks">[5]</span></div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">Determine whether \(\mathrm{f}\) is an increasing or a decreasing function. Explain your answer.<span class="inline-marks">[2]</span></div></li></ol>

The equation of the curve is \(y = \mathrm{f}(x)\), where \(\mathrm{f}(x) = (x + 4)\sqrt{2x - 3}\), \(x > \frac{3}{2}\).

Show that \(\mathrm{f}'(x) = \frac{px + q}{\sqrt{2x - 3}}\), where \(p\) and \(q\) are integers.

Find the \(x\)-coordinates of the points where the gradient of the normal is \(-\frac{1}{7}\).

Determine whether \(\mathrm{f}\) is an increasing or a decreasing function. Explain your answer.

Applications of Differentiation

Applications of Differentiation