POSSIBLE APPROACHES<br />
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  CLASS QUESTIONS<br />

  <ul>
    <li>Can you think of functions for which this sort of approach
    might not work?</li>

    <li>Does this method tell us anything about the number of roots
    of an equation?</li>
  </ul><br />
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  CONCEPT NOTES<br />

  <ul>
    <li>This is a quick problem in which students should be
    encouraged to try out function evaluation for various choices
    of numbers. Remember, that the key point is whether the
    function is positive or negative: we don't need to evaluate the
    exact values.</li>

    <li>For interested students you might wish to say that at
    university this sort of idea is extended in courses on
    Analysis, and this result is called the Intermediate Value
    Theorem. It is actually a very useful and powerful mathematical
    idea.</li>
  </ul><br />
  PROCESS NOTES<br />
  This problem suggests trial and error <br />
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  CONTENT NOTES<br />
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  EXTENSIONS<br />
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  For example: it is easy to see that 
  






 
  
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mn>72</mn>
<msup><mrow><mi>x</mi></mrow><mrow><mn>5</mn></mrow>
</msup>

<msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>2</mn></mrow>
</msup>
<mo>-</mo><mn>1</mn></mrow></math>is positive for 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>x</mi><mo>=</mo><mn>1</mn></mrow></math>, 
    <p/>    

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  Interesting discussion questions / points are:<br />

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    PROCESS
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    CONTENT
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