<p>Let&nbsp;\(f(x) = \frac{1}{3}x^3 - x^2 -3x\). Part of the graph of \(f\) is shown below.</p>
<div class="graph-block" data-graph-config="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" data-width="250" data-height="200" style="width:250px;height:200px;max-width:100%;display:block;margin:0 auto;"></div>
<p>There is a maximum point at \(\mathrm{A}\) and a minimum point at \(\mathrm{B} (3, -9)\).</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Find the coordinates of \(\mathrm{A}\).<span class="inline-marks">[8]</span></div></li><li><div class="list-item-paragraph">Write down the coordinates of<span class="inline-marks">[6]</span></div><ol class="i-list"><li><div class="list-item-paragraph">the image of \(\mathrm{B}\) after reflection in the \(y\)-axis;</div></li><li><div class="list-item-paragraph">the image of \(\mathrm{B}\) after translation by the vector \( \begin{pmatrix} -2 \\ 5 \end{pmatrix}\);</div></li><li><div class="list-item-paragraph">the image of \(\mathrm{B}\) after reflection in the \(x\)-axis followed by a horizontal stretch with scale factor \(\frac{1}{2}\).</div></li></ol></li></ol>

Let \(f(x) = \frac{1}{3}x^3 - x^2 -3x\). Part of the graph of \(f\) is shown below.

There is a maximum point at \(\mathrm{A}\) and a minimum point at \(\mathrm{B} (3, -9)\).

Functions

International Baccalaureate Standard Level Mathematics