Equivalent definitions of differentiable I am trying to show:
The two statements are equivalent: 
(i) $f$ is diﬀerentiable at $a$, 
(ii) $f(a + h) = f(a) + ch + o(h)$,
where c is some constant (depending on $a$) and $o(h)$
denotes some function of $h$ (also depending on $a$), with the property that
$$\lim_{h\to 0} \frac{o(h)}{|h|} = 0$$
(That is $o(h) = h\alpha(h)$; where $\lim_{h\to0} \alpha(h) = 0$)
What is the relation between $c$ and $f′(a)$?
For (i) I have given the standard definition of differentiable in terms of limit. I see this is not too different from the statement in (ii) but I cannot make them equivalent.
Any help would be much appreciated.

Hint: First try to prove that i) follows from ii). Knowing that $f(a+h)=f(a)+ch+o(h)$, calculate $f'(a)$ by definition. 
