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  <question type="description">
    <name>
      <text>10.2.9 (Example of finding equation of tangent line)</text>
    </name>
    <questiontext format="moodle_auto_format">
      <text><![CDATA[<h3>Example</h3>

<p>Find the equation of the tangent to \(f(x) = x^2+1\) at the point where \(x = 1\). </p>

<h3>Solution</h3>

<p>Since \(f(1) = 1^2 +1 = 2\), the point where the tangent touches the curve is \((1,2)\). Now, \(f'(x) = 2x\) so at \(x = 1\), \(f(1) = 2\), thus the gradient at the of the tangent at the point is \(2\). Therefore, using the formula above, the tangent has equation 
\[
y = 2(x-1) +2 \implies y = 2x
\]</p>]]></text>
    </questiontext>
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    <hidden>0</hidden>
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