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<quiz>
  <question type="stack">
    <name>
      <text>10.0.19 (Finding gradient of tangent at a point one power 2)</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Find the gradient of the tangent to the curve \(f(x)= x^{@pp@}\) at the point \(({@xx@},{@yy@})\).</p>

<p>[[input:ans1]][[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>We will use the observation above, so let \(A\) be the point \(({@xx@},{@yy@})\) and \(B\) be the point \({@xh@}, f({@xh@})\) = \(({@xh@}, {@f1@})\). Thus the gradient of the tangent at the point A is 
\[
\begin{align*}
\mbox{gradient } &= \lim\limits_{h \to 0} \frac{f({@xh@}) -f({@xx@})}{h}
\\
&= \lim\limits_{h \to 0} \frac{{@f1@} - {@yy@}}{h}
\\
&= \lim\limits_{h \to 0} {@lim1@}
\\
&=\lim\limits_{h \to 0} ({@lim2@})
\\
&= {@ta1@}
\end{align*}
\]</p>]]></text>
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    <idnumber/>
    <stackversion>
      <text>2020081700</text>
    </stackversion>
    <questionvariables>
      <text>pp:rand([2,3]);

xx: 1+rand(20);
xh: xx+h;
func:x^pp;
yy: ev(func,x=xx);

f1: ev(func, x=xh);

lim1: (f1-yy)/h;

lim2: expand(lim1);

ta1: ev(lim2,h=0);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>{@func@} at point ({@xx@},{@yy@}) has derivative {@ta1@}.</text>
    </questionnote>
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      <text/>
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      <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>
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    <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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    <complexno>i</complexno>
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