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Suppose $f:\mathbb{R}\rightarrow\mathbb{R}$ is a $C^{2}$ function. Is true that for every $x, there exists $\theta\in(x,x+h)$, such that $f(x+h)-f(x)=f'(x)h+\frac{1}{2}f''(\theta)h^2$

Im studying optmization and the author uses this fact in $\mathbb{R}^{n}$, so i think that if i can prove this in $\mathbb{R}$, hence the adaptation is easy, but is that true?

Thanks

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    I had never paid enough attention to this rest. Now i understand. Thanks all2012-10-23

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This is just the Lagrange form of the remainder for Taylor's Theorem.