# Differentiation Proof

1. Sep 24, 2009

### dgonnella89

1. The problem statement, all variables and given/known data
Prove if f(x) is differentiable at x=a then $$f'(a)=lim_{h\rightarrow0}\frac{f(a+h)-f(a-h)}{2h}$$

2. Relevant equations
I know that the derivative is defined as
$$f'(a)=lim_{x\rightarrow a}\frac{f(x)-f(a)}{x-a}$$

3. The attempt at a solution
Starting from the definition I used a known relation.
$$f'(a)=lim_{x\rightarrow a}\frac{f(x)-f(a)}{x-a}=lim_{h\rightarrow0}\frac{f(a+h)-f(a)}{h} =lim_{h\rightarrow0}\left[\frac{f(a+h)-f(a-h)}{h}+\frac{f(a-h)-f(a)}{h}\right]$$

I'm not sure how to decompose anymore from here. Any help you could give would be greatly appreciated.

2. Sep 24, 2009

### tiny-tim

Hi dgonnella89!

Hint: put k = -h in the definition of f'(a).

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