<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="description">
    <name>
      <text>10.0.17 (Example of finding gradient at particular point)</text>
    </name>
    <questiontext format="moodle_auto_format">
      <text><![CDATA[<h3>Example</h3>

<p>Find the gradient of the tangent to the curve \(f(x)= x^2\) at the point \((2,4)\).</p>

<h3>Solution</h3>

<p>We will use the observation above, so let \(A\) be the point \((2,4)\) and \(B\) be the point \(2+h, f(2+h)\) = \((2+h, (2+h)^2)\). Thus the gradient of the tangent at the point A is 
\[
\begin{align*}
\mbox{gradient } &= \lim\limits_{h \to 0} \frac{f(2+h) -f(2)}{h}
\\
&= \lim\limits_{h \to 0} \frac{(2+h)^2 -4}{h}
\\
&= \lim\limits_{h \to 0} \frac{4 +4h +h^2 - 4}{h}
\\
&= \lim\limits_{h \to 0} \frac{h(4+h)}{h}
\\
&= \lim\limits_{h \to 0} 4 + h \:\:\:\:\: \mbox{as } h \ne 0
\\
&= 4
\end{align*}
\]</p>]]></text>
    </questiontext>
    <generalfeedback format="moodle_auto_format">
      <text/>
    </generalfeedback>
    <defaultgrade>0</defaultgrade>
    <penalty>0</penalty>
    <hidden>0</hidden>
    <idnumber/>
  </question>
</quiz>
