Determine an interval $[a,b]$ on which the fixed-point ITERATION will converge.
$x = g(x) = (2 - e^x + x^2)/3$
I've determined that $g'(x) = (2x -e^x)/3$, but I don't know how to determine the interval without the guess-and-check method (which is not what I'm supposed to do). The question provided a hint saying "You may need some calculus concepts to work this out." However, I haven't the slightest as to which concepts it's referring to. I have the Fixed Point Convergence Theorem sitting next to me, but it is not offering much guidance.