Taylor polynomial maximum error.

hello, I was given this code that evaluates several Taylor polynomials and their errors for increasing degrees. The particular function being approximated is exp(x) on [-b,b].

   % TITLE: Evaluate Taylor polynomials for exp(x) about x = 0
  %
  % This evaluates several Taylor polynomials and their errors
  % for increasing degrees. The particular function being
  % approximated is exp(x) on [-b,b].
  % Initialize
  clc,clear all, close all
  b = input('Give the number b defining the interval [-b,b], b= ');
  if isempty(b)
      b
      disp('b is not defined')
          break
  end
  h = b/10;
  x = -b:h:b;
  max_deg = 4;
  % Produce the Taylor coefficients for the function exp(x) when
  % expanded about the point a = 0. The coefficients are stored
  % in the array c, which will have length max_deg+1.
  c = ones(max_deg+1,1);
  fact = 1;
  for I = 1:max_deg
  fact = I*fact;
  c(I+1) = 1/fact;

end
x
c

% Calculate the Taylor polynomial

p1 = polyeval(x,0,c,1);
p2 = polyeval(x,0,c,2);
p3 = polyeval(x,0,c,3);
p4 = polyeval(x,0,c,4);
% Calculate the errors in the Taylor polynomials
true= exp(x);
err1 = true-p1;
err2 = true-p2;
err3 = true-p3;
err4 = true-p4;
% Print the errors in tabular format
diary exp_taylor.txt
disp('   x        exp(x)     err1          err2          err3          err4')
for I = 1:length(x)
fprintf('%7.3f%10.3f%14.3e%14.3e%14.3e%14.3e\n', ...
         x(I),true(I),err1(I),err2(I),err3(I),err4(I))
end
diary off
figure(1)
plot(x,err1,x,err2,x,err3,x,err4)
legend('e^x-p_{1}(x)','e^x-p_{2}(x)','e^x-p_{3}(x)','e^x-p_{4}(x)',...
        'Location','Best')
figure(2)
plot(x,err1,'k-',x,err2,'k--',x,err3,'k:',x,err4,'k-.')
legend('e^x-p_{1}(x)','e^x-p_{2}(x)','e^x-p_{3}(x)','e^x-p_{4}(x)',...
        'Location','Best')

and polyeval is given as

function value= polyeval(x,alpha,coeff,n)
%
%function value= polyeval(x,alpha,coeff,n)
%
% Evaluate a Taylor polynomial at the points given in x, with
% alpha the point of expansion of the Taylor polynomial, and
% with n the degree of the polynomial. The coefficients are to
%be given in coeff; and it is assumed there are n+1 entries in
% coeff with coeff(1) the constant term in the polynomial
value= coeff(n+1)*ones(size(x));
z = x-alpha;
for I = n:-1:1
    value = coeff(I) + z.*value;
end
end

Then, I was asked to modify the script to evaluate the maximum error for different values of x and the degree of the polynomials n (n=1,2,3,4) by using this formula

I would really appreciate it if you could give me some tips on how to start edting the scrpit to get the maximum error.

Thank you in advance.