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mathishard

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**2nd derivative proof..help please?**

hi, this will be my first post on the forum, although i in the past have looked over it!

um, this is NOT a homework problem, but is a problem in my textbook that i attempted to do.

it asks to show that if , for a function f, a second derivative exists at x0

to prove that

f''(x0) = lim h->0 [f(x0+h)-f(x0-h)-2f(x0)] / h^2

...At first i thought this would be easy, just using

f ' (x0) = limh->0 ( f(x0+h)-f(x0)) / h

and f''(x0) = lim (f'(x0+h)-f'(x0))/h

but somehow i haven't been able to get the expression they ask for? am i missing something?? (a trick)? thanks!