function  [L,n]=difflim(f,x,toler)

%Input  - f is the function to differentiate
%       - x is the differentiation point
%       - toler is the desired error tolerance
%Output - L=[H' D' E']: H is the vector of step sizes
%                       D is the vector of approximate derivatives
%                       E is the vector of error bounds
%       - n is the coordinate of the "best approimation"


max1=15;
h=1;
H(1)=h;
D(1)=(feval(f,x+h)-feval(f,x-h))/(2*h);
E(1)=0;
R(1)=0;

for n=1:2
   h=h/10;
   H(n+1)=h;
   D(n+1)=(feval(f,x+h)-feval(f,x-h))/(2*h);
   E(n+1)=abs(D(n+1)-D(n));
   R(n+1)=2*E(n+1)*(abs(D(n+1))+abs(D(n))+eps);
end

n=2;

while((E(n)>E(n+1))&&(R(n)>toler))&&n<max1
   h=h/10;
   H(n+2)=h;
   D(n+2)=(feval(f,x+h)-feval(f,x-h))/(2*h);
   E(n+2)=abs(D(n+2)-D(n+1));
   R(n+2)=2*E(n+2)*(abs(D(n+2))+abs(D(n+1))+eps);
   n=n+1;
end

n=length(D)-1;
L=[H' D' E'];