Mean-Value Theorem
المؤلف:
Gradshteyn, I. S. and Ryzhik, I. M
المصدر:
ables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press
الجزء والصفحة:
...
29-9-2018
2138
Mean-Value Theorem
Let 
be differentiable on the open interval 
and continuous on the closed interval ![[a,b]](http://mathworld.wolfram.com/images/equations/Mean-ValueTheorem/Inline3.gif)
. Then there is at least one point 
in 
such that
The theorem can be generalized to Cauchy's mean-value theorem.
REFERENCES:
Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, pp. 1097-1098, 2000.
Jeffreys, H. and Jeffreys, B. S. "Mean-Value Theorems." §1.13 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, pp. 49-50, 1988.
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