- #1

Euklidian-Space

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## Homework Statement

Let ##I \subset \mathbb{R}## be an open interval and let ##f:I \rightarrow \mathbb{R}## be differentiable on I. Show that if ##f''(a)## exists, then ##f''(a) = \lim_{h \rightarrow 0}\frac{f(a + h) - 2f(a) + f(a - h)}{h^2}##

## Homework Equations

## The Attempt at a Solution

I tried tackling this by using limit definition of the derivative for ##f''(a)##.

$$f''(a) = \lim_{h \rightarrow 0}\frac{f'(a + h) - f'(a)}{h}$$[/B]

and then maybe use limit definition again for the terms in the numerator above? maybe use L'hopitals's rule? Not sure