1. ## Fixed point iteration

Hey guys,

I'm struggling a bit with this problem. Just confused I guess.

Background:
The equation $f(x) = e^x - 3x^2 = 0$ has 3 roots. To determine the roots by fixed point iteration we can rearrange the equation to obtain the iteration formulas: $x = g(x) = \pm \sqrt{\frac{e^x}{3}}$
Question:
Determine analytically the largest interval $[a,b]$, so that for any $p_0 \ \text{element of} \ [a,b]$ the iteration formula with the minus sign will converge to a root close to -0.5. You must therefore find the largest interval on which the conditions of the Fixed Point theorem are satisfied.
I've drawn the graphs (see attached), and $g(x)$ approaches 0 as x approaches negative infinity. But it doesn't make sense to me that the interval can be [-inf, b] where b is the rightmost bound of the interval.

I'm just very confused I guess. Can I get a push in the right direction?