An interval must contain a root of the equation f(x)=0 if...
there is a sign change.
the two bounds of the interval are 0.
the difference between the bounds is 1.
the signs are the same.
To solve an equation of the form f(x)=0 by an iterative method...
rearrange f(x)=0 into a form x=g(x).
do the inverse of the function.
rearrange f(x)=0 into a form x=f^-1(x).
rearrange f(x)=0 into a form g(x)=f(x)^-1
Different rearrangements of the equation f(x)=0 will always lead to the same root.
