Help finding a derivative using tolerance and while loop

I need to make an m-file myderivative(f,a,tol) where f is a function handle for x, a is a real number and tol is a small positive number. I need the file to approximate f'(a) by finding (f(a+h)-f(a))/h for h=1,1/2,1/3,1/4.... until successive values differ by less than tol using a while loop.

Even though I know this isn't right, I have:

 function r=myderivative(f,a,tol)
y=subs(diff(f),x,a);
for n=1:inf;
    h=1/n;
while (1/n+1)-h<tol;
    (f(a+h)-f(a))/h;
end
end
r=y

Answer 1

[Geoff Hayes]

Renee - start with just the basic outline of your function. You have the signature and you need a while loop. Rather than having one that goes to infinity, set an upper bound on the maximum number of iterations just so that your code doesn't get stuck (this is a good practice to get into when using while loops)

 function r=myderivative(f,a,tol)

 % initialize the output to something
 y = 0;

 % only allow 500 iterations
 maxIters = 500;
 n        = 1;

 while n<=maxIters

     % set h
     h = 1/n;

     % do the real work here

     % increment n
     n = n + 1;
 end

So now you have a basic loop that doesn't really do anything, but you'll never get stuck in an infinite loop.

Now your code must approximate f'(a) by finding (f(a+h)-f(a))/h for h=1,1/2,1/3,1/4.... until successive values differ by less than tol. So the above code is missing the calculation of f(a+h)-f(a))/h and some sort of comparison. What should that comparison be?