it is known thm of interpolation that:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{f[x_1, x_2] - f[x_0, x_1]}{x_2 - x_0}[/tex] = f"(c)}/2

where c is between the minimum and maximum of [tex]x_0, x_1, x_2[/tex]

and where

[tex]f[x_0, x_1] = \frac{f(x_1) - f(x_0)}{x_1 - x_0} = f'(d) [/tex] where d is between [tex] x_0[/tex] and [tex] x_1 [/tex] by the mean value theorem.

Is it possible and if so, can anyone halp me prove this equality:

[tex]\frac{f[x_1, x_2] - f[x_0, x_1]}{x_2 - x_0}[/tex] = f"(c)/2

using possibly Rolle's Thm, the Mean Value Thm, the Taylor series expansion, among others? (i.e., using only elelmentary calculus)

thanks

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# Homework Help: Proof using Rolle's thm or the Mean Value Thm

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