# Mean Value Theorem

Why is it that if you have $$\frac{f(x_1) - f(x_2)}{x_1-x_2} = f'(\xi)$$ then $$\xi = x_1 + \theta(x_2-x_1)$$ where $$0<\theta<1$$?

Thanks

## Answers and Replies

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What does the mean value theorem say about what values $$\xi$$ can take?

It says that $$x<\xi<x+h$$

in you problem $$x_{1} = x$$ and $$x_{2} - x_{1} = h$$
therefore, $$\xi = x_1 + \theta(x_2-x_1)= x + \theta h$$ where $$0<\theta<1$$
does it make sense now?

yep. thanks a lot