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Mean Value Theorem

  1. Jan 27, 2005 #1
    Why is it that if you have [tex] \frac{f(x_1) - f(x_2)}{x_1-x_2} = f'(\xi) [/tex] then [tex] \xi = x_1 + \theta(x_2-x_1) [/tex] where [tex] 0<\theta<1 [/tex]?

    Thanks
     
  2. jcsd
  3. Jan 27, 2005 #2

    learningphysics

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    What does the mean value theorem say about what values [tex]\xi[/tex] can take?
     
  4. Jan 27, 2005 #3
    It says that [tex] x<\xi<x+h [/tex]
     
  5. Jan 27, 2005 #4
    in you problem [tex] x_{1} = x[/tex] and [tex]x_{2} - x_{1} = h [/tex]
    therefore, [tex] \xi = x_1 + \theta(x_2-x_1)= x + \theta h [/tex] where [tex] 0<\theta<1 [/tex]
    does it make sense now?
     
  6. Jan 27, 2005 #5
    yep. thanks a lot
     
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