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Mean Value Theorem

  • #1
1,235
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
 

Answers and Replies

  • #2
learningphysics
Homework Helper
4,099
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What does the mean value theorem say about what values [tex]\xi[/tex] can take?
 
  • #3
1,235
1
It says that [tex] x<\xi<x+h [/tex]
 
  • #4
609
0
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?
 
  • #5
1,235
1
yep. thanks a lot
 

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