The Question: Let's approximate the root $p \in [0,1]$ by applying fixed point iteration. Consider the iteration function $g(x) = 1 - x^{2}. $ Can you find an interval which the fixed point theorem can be applied ?
The Attempt: I have tried using the Bisection Method to figure out the root of the function $h(x) = 1 - x - x^{2}$. However, when I do this, I am not getting any values that belong to the intervals when I compute for the iterations. Is there some other way I can find an interval that I can apply the fixed point theorem to?
Thank you for the help!!
Hint: If I have understood the statement correctly the answer is no. The reason being that at the fixed point the derivative of $g$ is smaller than $-1$.