Finding Multiplicity of a function using Newtons method

Hi there, I am asked to find the roots of a function using modified newtons method but that requires the prior knowledge of the multiplicity of a function. I find this by using the rule in the png.

and the code i wrote for it:

function m=multiplicity(f,a)
syms x
m=0;
while round(f(a)) == 0
    m=m+1;
    f = matlabFunction(diff(sym(f)));
    try 
        f(a);
    catch
        break
    end    
end
end

however I am told that I need to find it from "the sequence of values in the iterations" i assume this means buy using the vector of x values found in the newtons method

i used this for loop

for k=1:length(X)-1
    m(k) = error(k+1)*df(X(i)/f(X(i));
end

where the error is the values of X minus the actual root and X is the values found with newtons method. This method seems to work for functions of multiplicity 1 but didn't work for (x-5)^2

can somebody please help?