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Homework Help: Local minimum

  1. Apr 23, 2010 #1
    The question asks for local minimum of x^4-9x^3+9x^2+5x-4.

    The answer was x=-0.21 and 5.96.

    I thought 5.96 is the absolute minimum, since it gives the loweset y value on the open interval. Where am I wrong.

  2. jcsd
  3. Apr 23, 2010 #2


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    An absolute minimum is a local minimum; if it's a minimum across the entire interval, it's obviously a minimum locally.
  4. Apr 23, 2010 #3
    So all absolute are also locals? Never knew that. Thanks.
  5. Apr 23, 2010 #4


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    You aren't wrong about x=5.96 being the absolute minimum. But the problem is asking for local minima. There's more than one.
  6. Apr 23, 2010 #5
    I just thought the other value is the absolute minimum, not the local minimum, so I didn't include it as the local minimum. So, the absolute is ALWAYS also a local one?
  7. Apr 23, 2010 #6


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    Sure it is. ideasrule has it correct.
  8. Apr 23, 2010 #7
    That's all I need. Thank you both.
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