Understanding the Mean Value Theorem in Calculus

[courtrigrad]

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

 

[learningphysics]

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

 

[courtrigrad]

It says that x<\xi<x+h

 

[vincentchan]

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?

 

[courtrigrad]

yep. thanks a lot