Evaluate a twice differentiable limit Evaluate $$\lim_{h \rightarrow 0} \frac{f(x+h) -2f(x) + f(x-h) } { h^2}$$
if $f$ is a twice differentiable function. 
I'm not sure how to understand this problem. If I differentiate the numerator I get $f'(x+h) - 2f'(x) + f'(x-h)$ but that doesn't seem to take me anywhere?

Hint
Rewrite
$$ [f(x+h) -2f(x) + f(x-h)] =[f(x+h)-f(x)] -[f(x)-f(x-h)]$$
Divide each portion by $h$. What does that become ? Do it again to arrive to ...
I am sure that you can take from here.
