need help to code this cubic fit

hello

i need some guidace to code the cubic fit optimization in matlab

i coded it initially like this

clc
clear all

syms X;
f=X.^4+2.*X+4;

d_dx = diff(f, X);

dd_dx = diff(d_dx, X);

i=2;
iter=10;

%xk=0;
xk(1)=0.1;
xk(2)=0.2;



u1=subs(d_dx,X,xk(1))+subs(d_dx,X,xk(2))-3*((subs(f,X,xk(1))-subs(f,X,xk(2)))/xk(1)-xk(2));
u2=sqrt(u1^2-subs(d_dx,X,xk(1))*subs(d_dx,X,xk(2)));

xk(3)=xk(2)-(xk(2)-xk(1))*((subs(d_dx,X,xk(2))+u2-u1)/((subs(d_dx,X,xk(2)))-(subs(d_dx,X,xk(1)))+2*u2));

 while i<iter
    i=i+1;
    u1=subs(d_dx,X,xk(i-1))+subs(d_dx,X,xk(i))-3*((subs(f,X,xk(i-1))-subs(f,X,xk(i)))/xk(i-1)-xk(i));
u2=sqrt(u1^2-subs(d_dx,X,xk(i-1))*subs(d_dx,X,xk(i)));

xk(i+1)=xk(i)-(xk(i)-xk(i-1))*((subs(d_dx,X,xk(i))+u2-u1)/((subs(d_dx,X,xk(i)))-(subs(d_dx,X,xk(i-1)))+2*u2));
    
%     
%     
 end

 xk