Maximum value

  • Thread starter Ted123
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  • #1
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Homework Statement



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]

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]
 

Answers and Replies

  • #2
45
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-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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