function [xnew,its]=newt(f,fp,xold,tol)

%NEWT   Newton's method
%   [xnew,its]=newt(f,fp,xold,tol) uses Newton's method for rootfinding. 
%   It returns a root, xnew, of f(x) (with derivative given by function fp(x))
%   using a starting guess xold. The stopping criteria is |f(x)|<tol. The 
%   number of iterations, its, is also returned.
%
% MMSC, October 2021

fxold=f(xold);
its=0;
while abs(fxold)>tol
    xnew=xold-fxold/fp(xold);
    xold=xnew;
    fxold=f(xold);
    its=its+1;
end
xnew=xold;