Originally Posted by

**arbolis** I've mostly solved the following problem :

The equation $\displaystyle x^2-x-1=0$ has a zero in $\displaystyle [-1,0]$.

a)Verify that the function $\displaystyle g(x)=x^2-1$ has $\displaystyle 2$ fixed points and that the derivative of g in a fixed point has its absolute value greater than $\displaystyle 1$. Take note that the existence of a fixed point doesn't imply that the derivative evaluated in this point has an absolute value lesser than 1. **DONE**

b)Show that $\displaystyle g(x)$ satisfies the conditions of existence of a fixed point in [-1,0]. **DONE **(I showed that g was contractive on this interval)