I'm just stuck on this problem :
We want to solve $\displaystyle f(x)=0$ via a function of iteration $\displaystyle x=g(x)$ that satisfies the necessaries conditions of convergence. Determine a bound of the error which is committed in each step in function of the difference between the 2 last values of the sequence. In other words, determine $\displaystyle C$ such that $\displaystyle |x_{n+1}-x_*|\leq C |x_{n+1}-x_n|$. Where $\displaystyle x_*$ is the zero that we are looking for.
Tip : Use the triangular inequality in the inverse sens than usual.
I don't know how to start. I'm stuck at starting it and I need it to solve the second part of the exercise.