How to prove whether a function is differentiable

[haha1234]

Homework Statement

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

Homework Equations

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

 

[dirk_mec1]

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

 

[pasmith]

Homework Statement

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

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

Homework Equations

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

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

 

[haha1234]

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



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

Sorry,but it maybe equals to 0.