I have to describe the famous newton-rapshon algorithm for finding a root of the function

this is what i came up with, i aint not familiar with matlab and programming at all, so this is somewhat a melt from a lot of matlab tutorials, I dont master the code, but what's really a challenge is understanding the errors

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function x = newton(fun,dfun,x0,tol,Nmax)

x = x0;

f(x) = feval(fun,x);

df(x)= feval(dfun,x);

steps = 0;

re = tol;

myrel = 1;

while myrel > re && (steps < Nmax)

xold = x;

x = x - f(x)/df(x);

steps = steps + 1;

myrel = abs((x-xold)/x);

end;

if myrel <= re

disp( 'Zero found at' )

disp( x )

else

disp( 'Zero NOT found' )

end;

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when i test it, i find 2 very strange facts

fact 1: it cannot handle non-integer, if I want to test the function in the prompt with sin and cos and x0=3 , it stops on the first iteration: 3,14255...

this is the error:

attempted to acces f(3.14255); index must be a positive inter or logical

My idea: i thought matlab had no problems at all with any kind of number, in c++(also a big noob at that) u have to declarate everything, but not so in matlab yes?)

and fact2

i only tested the function with sin, cos and 3

when i test it with a simple Polynomial, let's say x²-2 for finding the value of square root of 2 it gives an error in the second line: f(x) = feval...

how can that line work with the first example and not with a simple polynomial in x,

can someone get me on track