<p>Consider \(f(x) = \frac{1}{3}x^3 +2x^2 - 5x\). Part of the graph of \(f\) is shown below. There is a maximum point at \(\mathrm{M}\), and a point of inflexion at \(\mathrm{N}\)</p>
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<ol class="abc-list"><li><div class="list-item-paragraph">Find \(f'(x)\).<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Find the \(x\)-coordinate of \(\mathrm{M}\).<span class="inline-marks">[4]</span></div></li><li><div class="list-item-paragraph">Find the \(x\)-coordinate of \(\mathrm{N}\).<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">The line \(L\) is the tangent to te curve of \(f\) at \( (3,12)\). Find the equation of \(L\) in the form \(y = ax +b\)<span class="inline-marks">[4]</span></div></li></ol>

Consider \(f(x) = \frac{1}{3}x^3 +2x^2 - 5x\). Part of the graph of \(f\) is shown below. There is a maximum point at \(\mathrm{M}\), and a point of inflexion at \(\mathrm{N}\)

Find the \(x\)-coordinate of \(\mathrm{M}\).

Find the \(x\)-coordinate of \(\mathrm{N}\).

The line \(L\) is the tangent to te curve of \(f\) at \( (3,12)\). Find the equation of \(L\) in the form \(y = ax +b\)

Mathematics

International Baccalaureate Mathematics: Applications and Interpretation Standard Level