<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>10.2.11 (Big slope of quadratic)</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>For what values of \(x\) is the slope of the function \(f(x) = {@f@}\) greater than or equal to {@k@}?</p><p>\(x \geq \) [[input:ans1]]. [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>The function \(f(x) = {@f@}\) has derivative \(f'(x) = {@df@}\).&nbsp; So we need \(x\) to satisfy \({@df@}\geq {@k@}\), which is satisfied if and only if \(x \geq \frac{{@k@} + {@-b@}}{{@2*a@}}={@ta@}\).<br></p>]]></text>
    </generalfeedback>
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    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2020081700</text>
    </stackversion>
    <questionvariables>
      <text>a: 1+rand(5);
b:-(1+rand(10));
c:1+rand(5);
k:rand(10);
f:a*x^2 + b*x + c;
df: diff(f,x);
ta: (k-b)/(2*a);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\(f(x) = {@f@}, f'={@df@}, x\geq{@ta@}.\)</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
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    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
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      <name>ans1</name>
      <type>algebraic</type>
      <tans>ta</tans>
      <boxsize>15</boxsize>
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        <name>0</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>ta</tans>
        <testoptions/>
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        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
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        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
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    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ta</value>
      </testinput>
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  </question>
</quiz>
