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Homework Help: Maximum value

  1. Feb 19, 2012 #1
    1. The problem statement, all variables and given/known data

    I'm asked to find the maximum value of [itex]h[/itex] such that [itex]\mu = \lambda h\;\;(\lambda \in \mathbb{R})[/itex] satisfies: [tex]|1+\mu + \frac{1}{2} \mu ^2 + \frac{1}{6} \mu ^3| < 1[/tex]

    3. The attempt at a solution

    My hurdle is solving [itex]1+\mu + \frac{1}{2} \mu ^2 + \frac{1}{6} \mu ^3=1[/itex] to find the interval [itex]\mu\in (?,?)[/itex] which satisfies [tex]|1+\mu + \frac{1}{2} \mu ^2 + \frac{1}{6} \mu ^3| < 1[/tex]
  2. jcsd
  3. Feb 19, 2012 #2
    -1 from both sides, then obviously μ=0 is a solution, and from there you should be able to find the rest of the intervals using the fact it's a positive cubic.
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