Local polynomial approximation of functions - Taylor polynomial ?

In my book I have example what I didnt know how to solve... Example: Construct the Taylor polynom for the function F (x) = (x - 1). (X - 2). (X - 3). (X - 4). (X - 5) = x.^5 - 15*x.^4 + 85*x.^3 - 225*x.^2 + 274.*x -120, in the middle u = 3 , for n = 1,3,5. Use this TaylorEval function :

---------------------------------------------------------------------------------------

function y = TaylorEval(t,u,x)
% TAYLOREVAL dava hodnoty Taylorovho polynomu vo vekt.argumente x
% y = TaylorEval(t,u,x), 
% ---------------------------------------------------------------
% argin : t = vector koef. Taylor. polynom in middle u
%         u = middle Tayl.pol.
%         x = vector who want to evoulate p(x))
% argout: y = vector Taylor.pol. in vector x
%
n = length(t);
y = t(1)*ones(1, length(x));
for i = 2:n
   y = (x - u).*y + t(i);
end
---------------------------------------------------------------------------------------
T(x,3,1) and T(x,3,3)   plot in interval [2,4]  must to get this plot:
http://i.imgur.com/M2gmlJv.jpg

>> I tried to solve like this:

u = 3;
n = [1 3 5];
p = poly([1 2 3 4 5]);  

% for i = 0:3
% pv = polyval(p,3)
% p1 = polyder(p);
% p  = p1;
% end

px1 = [-30  0  4  0];
x   = linspace(2,4,201);
y   = x.^5 - 15*x.^4 + 85*x.^3 - 225*x.^2 + 274.*x -120;
z1   = TaylorEval(px1,3,x);

plot(x,y,'b',x,z1,'r:')
% xlim([-2,4])
% ylim([-4,4])
shg

and I get in plot: http://i.imgur.com/Vih48gP.png

Answer 1

[x y]

Now I get same with this:

px1 = [4  0];
px2 = [-5 0 4  0];
x   = linspace(2,4,201);
y   = x.^5 - 15*x.^4 + 85*x.^3 - 225*x.^2 + 274.*x -120;
z1   = TaylorEval(px1,3,x);
z2 = TaylorEval(px2,3,x);

plot(x,y,'b',x,z1,'r:',x,z2,'r:')