Mean value theorem

  • Adi Ben-Israel
  • Robert Gilbert
Part of the Texts and Monographs in Symbolic Computation book series (TEXTSMONOGR)


The derivative of a function f at a point ξ
$$f'\left( \xi \right) = \mathop {\lim }\limits_{\Delta x \to 0} {\rm{ }}{{f\left( {\xi + \Delta x} \right) - f\left( \xi \right)} \over {\Delta x}},$$
is the slope of the line tangent to the graph of f at the point P = (ξ ,f (ξ)). Restricting to Δx > 0 we see that f′(ξ) is the limit of the slopes of secants PQ, as QP from the right (Fig. 7.1 a).


Iterative Method Initial Point Newton Method Unique Fixed Point Iteration Function 
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Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • Adi Ben-Israel
    • 1
  • Robert Gilbert
    • 2
  1. 1.Rutgers Center for Operations Research and Department of MathematicsRutgers UniversityNew BrunswickUSA
  2. 2.Department of Mathematical Science and Computer and Informational SciencesUniversity of DelawareNewarkUSA

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