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Let $f$ be a function defined on an interval $(a,b)$ and let $c \in (a,b)$. Suppose that $f$ is twice differentiable at $c$. Prove that $\displaystyle \lim_{h \rightarrow 0^+} \frac{(f(c+h)-2f(c)+f(c-h))}{h^2}= f''(c)$.

I tried this question but I could not prove righorously. Please Help.

ancient mathematician
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Anwesha1729
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  • Hint: Taylor expansion. – Mark Sep 24 '20 at 09:37
  • Check this: https://math.stackexchange.com/questions/210264/second-derivative-formula-derivation or this: https://math.stackexchange.com/questions/713260/evaluate-a-twice-differentiable-limit – Martin R Sep 24 '20 at 09:40

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