
Taylor's Theorem
Consider the forward difference approx. to f'
f'(0)= f(h)f(0) / h
Let the error be E = f'(0) (f(h)f(0) / h)
Derive a formula for E by Taylor expanding f about x0=0 and using the Remainder thm.
So far I have f(x)=f(x0) + f'(x0)h+f''(x0)h^2 /2 + f'''(c)h^3 /6
So the error will be f'''(c)h^3 /6 for some c in the interval
What do I do now?

Re: Taylor's Theorem
shouldn't it be f(h) = f(0) + f'(0)h + f"(c)h^2/2, for some c in (0,h)?

Re: Taylor's Theorem
You're right. But my error term is the same, f'''(0)h^3 /6
My error is supposed to be of the form K1h+k2h^2 and I'm not sure how to get there...

Re: Taylor's Theorem
if f(h) = f(0) + f'(0)h + f"(0)h^2/2 + f'''(c)h^3/6, then
then
f(h)  f(0) = f'(0)h + f"(0)h^2/2 + f'''(c)h^3/6
[f(h)  f(0)]/h = f'(0) + f"(0)h/2 + f'''(c)h^2/6
f'(0)  [f(h)  f(0)]/h = f"(0)h/2  f'''(c)h^2/6

Re: Taylor's Theorem
I was making a very stupid mistake. Thanks for helping!