I know that the local error at each step of Euler's method is O(t^2), where t is the time step. And since there are (b-a)/t steps, the order of the global error is O(t).
However, I saw a derivation of the global error by saying:
[f(x+t) - f(x)] / t = f'(x) + O(t)
Where O(t) represents the rest of the Taylor series expansion for f. My question is: how does this show that the global error is O(t)? Isn't this just showing that the slope's error is O(t)?