Hello,

One question that the professor of my calculus course likes to include in his exams is, if a certain function f(x) can be derived at a certain point (e.g. x=0).

In order to find this out, do I always have to find the limit $\displaystyle \lim\limits_{h\rightarrow0}\frac{f(x_0+h)-f(x_0)}{h}$ or can I also just find the derivative and then look at the limit $\displaystyle \lim\limits_{x\rightarrow x_0}f'(x)$?