%
% Written by:
% --
% John L. Weatherwax                2009-04-21
%
% email: wax@alum.mit.edu
%
% Please send comments and especially bug reports to the
% above email address.
%
% Problem on EPage 63; Solutions on EPage 161
%
%-----

close all; clc; clear all; 

addpath('../../BookCode');

format long;

n = 6;
for( k=3:n )
  coefs = zeros(1,k);
  for( l=0:k )
    coefs(l+1) = (-1)^l * ( 1/factorial(l) )^2 ;
  end
  % order so that the coefs(1) is the coefficient of highest degree and 
  % coefs(end) is the coefficient of lowest degree 
  % then we can use polyval with them
  % 
  coefs = fliplr( coefs );
  fn = @(x) polyval( coefs, x );
  
  if( false )
    coefs_degrees = k:-1:0;
    fn_prime_coefs = coefs_degrees .* coefs; 
    fn_prime_coefs = fn_prime_coefs(1:end-1); % drop the constant term (its derivative is zero)
  end
  
  fn_prime = @(x) polyval( fn_prime_coefs, x );
  
  fzero( fn, 1 )
end

format short;