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<quiz>
  <question type="stack">
    <name>
      <text>10.2.10 (Tangent lines)</text>
    </name>
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      <text><![CDATA[<p>Find the equation of the line tangent to the graph of \(f\) at the point \(({@aa@}, f({@aa@}))\), if \(f({@aa@})={@bb@}\) and \(f'({@aa@}) = {@cc@}\).&nbsp; Your answer should involve a variable \(x\).<br></p><p>\( y = \) [[input:ans1]] [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>The gradient of the tangent line to \(f\) at the point \({@aa@}\) is given by the derivative \(f'({@aa@}) = {@cc@}\). So the equation has the form \(y = {@cc@}x + c\) for some \(c\) which we have to compute.</p><p>But we know that \(f({@aa@}) = {@bb@}\), and the tangent line meets the graph of \(f\) at that point, so we must have that \({@bb@} = {@cc@}\cdot{@aa@} + c\), i.e. that \(c = {@AA@}\).<br></p><p>Hence, the equation of the line tangent to the graph of \(f\) is \( y = {@ta1@}.\)</p><p></p>]]></text>
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    <idnumber/>
    <stackversion>
      <text>2020081700</text>
    </stackversion>
    <questionvariables>
      <text>aa: rand(5)+1;
bb: rand_with_prohib(2,15,[a])
cc: rand_with_prohib(-5,5,[0,a,b])

AA: bb-cc*aa
ta1: cc*x+AA</text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\(f({@aa@})={@bb@}\), \(f'({@aa@}) = {@cc@}\) so \( y = {@ta1@} \)</text>
    </questionnote>
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      <text/>
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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>
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    <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>
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    <decimals>.</decimals>
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      <type>algebraic</type>
      <tans>ta1</tans>
      <boxsize>15</boxsize>
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        <answertest>AlgEquiv</answertest>
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    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ta1</value>
      </testinput>
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        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-1-T</expectedanswernote>
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      <testcase>2</testcase>
      <description/>
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        <name>ans1</name>
        <value>ta1+1</value>
      </testinput>
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        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-1-F</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
