<p>A function \(f\) has its first derivative given by \(f'(x) = (x - 3)^3\).</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Find the second derivative.<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Find \(f'(3)\) and \(f''(3)\).<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">The point \(\mathrm{P}\) on the graph of \(f\) has&nbsp;\(x\)-coordinate \(3\). Explain why \(\mathrm{P}\) is not a point of inflexion,<span class="inline-marks">[2]</span></div></li></ol>

A function \(f\) has its first derivative given by \(f'(x) = (x - 3)^3\).

The point \(\mathrm{P}\) on the graph of \(f\) has \(x\)-coordinate \(3\). Explain why \(\mathrm{P}\) is not a point of inflexion,

Mathematics

International Baccalaureate Mathematics: Applications and Interpretation Standard Level