# How to prove whether a function is differentiable

1. Feb 10, 2014

### haha1234

1. The problem statement, all variables and given/known data

Suppose that f is differentiable at x . Prove that ƒ(x)=lim[h→0] $\frac{ƒ(x+h)-ƒ(x-h)}{2h}$

2. Relevant equations

3. The attempt at a solution
I think that it may be proved by first principle,but I cannot rewrite the limit into the form of lim[h→0] $\frac{ƒ(x+2h)-ƒ(x)}{2h}$
So how can I solve this question?
THANKS

2. Feb 10, 2014

### dirk_mec1

You probably mean f'(x). You can rewrite it via u = x-h.

3. Feb 10, 2014

### pasmith

I assume this is $f'(x) = ...$

Use $f(x+h) - f(x-h) = (f(x+h) - f(x)) + (f(x) - f(x-h))$

4. Feb 10, 2014

### haha1234

Sorry,but it maybe equals to 0.