<p>Let&nbsp;\(g(x)= \frac{\ln{x}}{x^2}\), for&nbsp;\(x&gt;0\).</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Use the quotient rule show that&nbsp;\(g'(x) = \frac{1 - 2\ln{x}}{x^3}\).<span class="inline-marks">[4]</span></div></li><li><div class="list-item-paragraph">the graph of \(g\) has a maximum point at \(\mathrm{A}\). Find the \(x\)-coordinate of \(\mathrm{A}\).<span class="inline-marks">[3]</span></div></li></ol>

Let \(g(x)= \frac{\ln{x}}{x^2}\), for \(x>0\).

Use the quotient rule show that \(g'(x) = \frac{1 - 2\ln{x}}{x^3}\).

the graph of \(g\) has a maximum point at \(\mathrm{A}\). Find the \(x\)-coordinate of \(\mathrm{A}\).

Derivatives of Exponential, Logarithmic and Trigonometric Functions

International Baccalaureate Mathematics: Applications and Interpretation Standard Level