Finding the Range for r in an Inequality: Tips and Tricks

[azdang]

I'm working on a problem in which I have to find a range for r. I have an upper bound on it, but I can't seem to get the lower bound.

Here is the inequality to start with:
$$\lambda$$r - r³ + $$\lambda$$ < 0

Eventually, I get it down to:
$$\lambda$$ < $$\frac{r^3}{r+1}$$

However, I need r by itself on one side, and I have no idea what to do. Is there anything I actually could do or am I stuck?

Another note: r>0 and $$\lambda$$>0. Thanks!

 

[Focus]

You need to solve $\lambda r -r^3+\lambda=0$ first.