def newton$($func$,$ x$0,$ ftol$=1$e$-12,$ xtola$=1$e$-7,$ maxiter$=100)$:

func is a Python function that takes in $x$ and returns $f(x)$ and $f^{\text{'}}(x),$ in that order.

For example

f$,$ df $=$ func $(x)$

$x0$ is an initial guess for the root.

ftol is tol ${?}_f$ in Criterion $2,$ xtola is tol ${?}_x$ in Criterion $1.$

maxiter is the maximum number of iterations allowed.

Use a while loop in the function, and return both the estimated root and the

number of iterations used in the while loop.