Consider solving the equation $\exp(x) - x - 1 = 0$.
It is obvious that $x^* = 0$ is a solution of the equation. Suppose you don't know this and you would like to approximate $x^*$ numerically by one of the following four methods. Which method will lead to a convergent algorithm for approximating $x^*$?
Why are the others not suitable?
The four methods are bisection method, fixed point iteration, Newton's Method, and Secant method.
Attempt: I tried each method on the equation but I have found that each converges which I know is not correct.
For fixed point iteration, I put the equation in the form $x = \exp(x) - 1$.
I don't know where to start in terms of the "inverval" to begin with i.e. with bisection the first thing I do is try $x=0$ and I get that it is the root. So am I done? Is bisection method the "correct" method in this case?