Solving for Maximum Value of h in \mu = \lambda h

[Ted123]

Homework Statement

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

The Attempt at a Solution

My hurdle is solving 1+\mu + \frac{1}{2} \mu ^2 + \frac{1}{6} \mu ^3=1 to find the interval \mu\in (?,?) which satisfies |1+\mu + \frac{1}{2} \mu ^2 + \frac{1}{6} \mu ^3| < 1

 

[HmBe]

-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.