<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="description">
    <name>
      <text>10.2.19 (Graphs of derivs)</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<h3>Graphs of derivatives</h3>

<p>From the graph of a function, we can find the graph of its derivative by thinking about when the original graph is increasing, decreasing or stationary, and what this means for the sign of the derivative.</p>

<table style="text-align: center; margin-left:auto; margin-right:auto;" cellpadding="10" border="1" bordercolor="#3a87ad">
<thead>
<tr style="background: #c1ddea">
<th scope="col">Function</th>
<th style="min-width:7em" scope="col">Derivative</th>
<th scope="col">Graph of derivative</th>
</tr>
</thead>
<tbody>
<tr>
<td>Stationary</td>
<td>\(f'(x)=0\)</td>
<td>Has a root here</td>
</tr>
<tr>
<td>Increasing</td>
<td>\(f'(x)&gt;0\)</td>
<td>Lies above the \(x\)-axis</td>
</tr>
<tr>
<td>Decreasing</td>
<td>\(f'(x)&lt;0\)</td>
<td>Lies below the \(x\)-axis</td>
</tr>
</tbody>
</table>
<br/>
<h3>Example</h3>

The graph \(y=f(x)\) has two stationary points, so the graph of the derivative will have two roots (at the \(x\)-coordinates of the stationary points). Thinking about the sign of \(f'(x)\) on the three intervals helps us to construct the graph of the derivative shown below.</p>
<br/>
<p style="text-align: center;"><img src="@@PLUGINFILE@@/2_4_graph_of_deriv%20%281%29.svg" alt="Graphing the derivative of a cubic curve" width="209" height="325" class="img-responsive atto_image_button_text-bottom"></p>]]></text>
<file name="2_4_graph_of_deriv (1).svg" path="/" encoding="base64">[encoded data, 79044 characters]</file>
<file name="2_4_graph_of_deriv.svg" path="/" encoding="base64">[encoded data, 57832 characters]</file>
    </questiontext>
    <generalfeedback format="html">
      <text/>
    </generalfeedback>
    <defaultgrade>0</defaultgrade>
    <penalty>0</penalty>
    <hidden>0</hidden>
    <idnumber/>
  </question>
</quiz>
