# Matlab Secant Method

Recall that Newton's Method is an iterative way of approximating a
zero of a function \(f\). The idea is that, given a starting
guess \(x_0\) and an error tolerance \(\tau\), we compute new estimates of the zero
of \(f\) using the formula
\[
x_{n+1} = x_n-f(x_n)/f'(x_n)
\]
for \(n=0,1,\ldots\)
We use this iteration until \(\vert x_n-x_{n-1}\vert\lt\tau\)
or until we give up trying.
Unfortunately, we do not know how to use Matlab to compute
the derivative of \(f\) (it can, we just have not done it).
Instead, we can choose some small number \(h\) and use the approximation
\[f'(x_n) \approx \frac{f(x_n)-f(x_n-h)}{h} \]
instead of \(f'\).
If we use successive estimates of the root, then the formula becomes
\[
x_{n+1}=\frac{x_{n-1}f(x_n)-x_nf(x_{n-1})}{f(x_n)-f(x_{n-1})}.
\]
This is called the secant rule.
Write a Matlab function `secant(f,init_guess,tolerance)` that finds the
zero of a function using this secant formulation.

A solution for the
final is available.