I know that the Runge Kutta methods are usually derived using Taylor Series expansion.
However, I don't understand why the Taylor Series is even necessary.
If we know $\frac{dy(t)}{dt}=f(t,y(t))$, then I think we should know any $f(t,y(t))$ at any point.
So, I wonder why we need to take the Taylor series like it does here:
