<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>12.3.1.2 Classify roots</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
<p>Given the graphs of the following functions, classify the roots into simple or double.</p>
<ol class="HELM_parts">
    <li>
        <p>\(f(x) = {@f@}\).</p>
        <figure class="HELM_figure">
[[jsxgraph]]
const brd = JXG.JSXGraph.initBoard(divid, {axis: true, boundingbox: [-6, 35, 6, -35], showCopyright: false});
const f = brd.jc.snippet('{#f#}', true, 'x', true);
brd.create('functiongraph', [f]);
[[/jsxgraph]]
        </figure>
        <p>The negative root is a [[input:ans1]] root. [[validation:ans1]] [[feedback:prt1]]</p>
        <p>The positive root is a [[input:ans2]] root. [[validation:ans2]] [[feedback:prt2]]</p>
    </li>
    <li>
        <p>\(g(x) = {@g@}\).</p>
        <figure class="HELM_figure">
[[jsxgraph]]
const brd = JXG.JSXGraph.initBoard(divid, {axis: true, boundingbox: [-5, 3, 5, -1], showCopyright: false});
const g = brd.jc.snippet('{#g#}', true, 'x', true);
plot = brd.create('functiongraph', [g]);
[[/jsxgraph]]
        </figure>
        <p>Each root is a [[input:ans3]] root. [[validation:ans3]] [[feedback:prt3]]</p>
    </li>
</ol>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<ol class="HELM_parts">
    <li>
        <p>\(f(x) = {@f@}\).</p>
        <figure class="HELM_figure">
[[jsxgraph]]
const brd = JXG.JSXGraph.initBoard(divid, {axis: true, boundingbox: [-6, 35, 6, -35], showCopyright: false});
const f = brd.jc.snippet('{#f#}', true, 'x', true);
brd.create('functiongraph', [f]);
[[/jsxgraph]]
        </figure>
        <p>Note that if a root is a local maximum or minimum or an inflection point then the derivative of the function must
            also be zero there. Hence, we can conclude that if a root is a local maximum or minimum or an inflection point
            then it cannot be simple.</p>
        <p>With this in mind, we can see from the graph that the negative root is a {@first(mcq_correct(ta1))@} root,
            while the positive root is a {@first(mcq_correct(ta2))@} root.
        </p>
    </li>
    <li>
        <p>\(g(x) = {@g@}\).</p>
        <figure class="HELM_figure">
[[jsxgraph]]
const brd = JXG.JSXGraph.initBoard(divid, {axis: true, boundingbox: [-5, 3, 5, -1], showCopyright: false});
const g = brd.jc.snippet('{#g#}', true, 'x', true);
plot = brd.create('functiongraph', [g]);
[[/jsxgraph]]
        </figure>
        <p>In this case, every root is also a local minimum. Therefore, every root is a double root.
    </p></li>
</ol>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2021120900</text>
    </stackversion>
    <questionvariables>
      <text><![CDATA[a1: rand_with_step(1, 3, 1);
a2: rand_with_step(-3, -1, 1);
b: rand(2);
if b = 0
    then (
        f: expand((x - a1)^2 * (x - a2)),
        ta1: [["simple", true], ["double", false]],
        ta2: [["simple", false], ["double", true]]
    )
    else (
        f: expand((x - a1) * (x - a2)^2),
        ta1: [["simple", false], ["double", true]],
        ta2: [["simple", true], ["double", false]]
    );

k: rand_with_step(1, 4, 1);
g: 1 + sin(k * x);
ta3: [["simple", false], ["double", true]];]]></text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\(f(x) = {@f@}, \quad g(x) = {@g@}\)</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <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>
    <multiplicationsign>none</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
    <isbroken>0</isbroken>
    <variantsselectionseed/>
    <input>
      <name>ans1</name>
      <type>dropdown</type>
      <tans>ta1</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords/>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>0</mustverify>
      <showvalidation>0</showvalidation>
      <options/>
    </input>
    <input>
      <name>ans2</name>
      <type>dropdown</type>
      <tans>ta2</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
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      <showvalidation>0</showvalidation>
      <options/>
    </input>
    <input>
      <name>ans3</name>
      <type>dropdown</type>
      <tans>ta3</tans>
      <boxsize>15</boxsize>
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      <mustverify>0</mustverify>
      <showvalidation>0</showvalidation>
      <options/>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>first(mcq_correct(ta1))</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
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        </falsefeedback>
      </node>
    </prt>
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      <name>prt2</name>
      <value>1.0000000</value>
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        <name>0</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans2</sans>
        <tans>first(mcq_correct(ta2))</tans>
        <testoptions/>
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        <falseanswernote>prt2-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <prt>
      <name>prt3</name>
      <value>1.0000000</value>
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        <answertest>AlgEquiv</answertest>
        <sans>ans3</sans>
        <tans>first(mcq_correct(ta3))</tans>
        <testoptions/>
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        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt3-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
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        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt3-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
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    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>first(mcq_correct(ta1))</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>first(mcq_correct(ta2))</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>first(mcq_correct(ta3))</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt2-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt3</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt3-1-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>first(mcq_incorrect(ta1))</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>first(mcq_incorrect(ta2))</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>first(mcq_incorrect(ta3))</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt2-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt3</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt3-1-F</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
