While Loop code not working?

Question: I have to create a function m file called myfirstzero(f,a) which takes two inputs:

f: A function handle which you may assume will represent a polynomial.

a: A real number.

Does: Uses a while loop to find the smallest n such f(n)(a) = 0. Note that this means the nth derivative at x = a and note that n = 0 is fair game, where the 0th derivative of a function is just the function itself.

Returns: This value of n.

This is my code:

function a = myfirstzero(f,a)
syms x;
n = 0;
d = abs(subs(f(x),a));
    while (d > 0);
        d = subs(diff(f(x),n),a);
        n = n+1;
    end
    a = n;
end

Testing: When I test the code with results =myfirstzero(@(x) x^3+2,0) I get a= 2 when the correct answer should actually be 1.

Can someone help me with fine tuning my code. It works with some of my test data but not all of it. Below is all the test data I have to test this code:

a = myfirstzero(@(x) 2*x^3-3*x^2-12*x+6,2)----> works
a =1
a = myfirstzero(@(x) x^3,0)----->works
a =0
a = myfirstzero(@(x) x^3+2,0)----> not work
a =1
a = myfirstzero(@(x) x^6-5*x^5-2*x^4-x^3+x^2-x+10,3)---->not work
a =7
a = myfirstzero(@(x) x^5-x^3,2)----->not work
a =6
a = myfirstzero(@(x) x^4-10*x^3+24*x^2,1)----->not work
a =2

Test data file is also attached.

Answer 1

[Bob]

Can anyone help me?

[Erik S.]

Don't see your test data file

[Bob]

Sorry forgot to attach but here. It is also included in my question.

Answer 2

[Claire Li]

For the first test data sample that doesnt work for you, it seemed like it was because it doesn't know to stop when n=1 because its also 0 when n=2?

Try adding a break somewhere

[Bob]

Adding the break gave me a different answer, that was still wrong.