<p>Consider \(f(x) = x^2 + \frac{p}{x}\) , \(x \neq 0\), where&nbsp;\(p\) is a constant.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Find \(f'(x)\).<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">There is a minimum value of \(f(x)\) when&nbsp;\(x = -2\). Find the value of \(p\).<span class="inline-marks">[4]</span></div></li></ol>

Consider \(f(x) = x^2 + \frac{p}{x}\) , \(x \neq 0\), where \(p\) is a constant.

There is a minimum value of \(f(x)\) when \(x = -2\). Find the value of \(p\).

Mathematics

International Baccalaureate Mathematics: Applications and Interpretation Standard Level