<p>The diagram below shows the graph of $y=\mathrm{f}(x)$. The curve has a minimum point at $\left( 1,\,\,-\frac{1}{2} \right)$ and crosses the $x$–axis at $\left( -2,\,\,0 \right)$, $\left( 0,0 \right)$ and $\left( 2,\,\,0 \right)$. The lines $x=-1$, $x=3$ and $y=-3$ are the asymptotes of the curve.</p>
<div class="graph-block" data-graph-config="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" data-width="400" data-height="350" style="width:400px;height:350px;max-width:100%;display:block;margin:0 auto;"></div>
<p>Sketch $\mathrm{f}'\left( x \right)$.<span class="inline-marks">[3]</span></p>

The diagram below shows the graph of $y=\mathrm{f}(x)$. The curve has a minimum point at $\left( 1,\,\,-\frac{1}{2} \right)$ and crosses the $x$–axis at $\left( -2,\,\,0 \right)$, $\left( 0,0 \right)$ and $\left( 2,\,\,0 \right)$. The lines $x=-1$, $x=3$ and $y=-3$ are the asymptotes of the curve.

Sketching Derivative Graphs

Applications of Differentiation

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

2015 CJC P2 Q2

2015 CJC P2 Q2

Video Solution:

Solution:

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