Rolle,s Theorem
المؤلف:
Apostol, T. M
المصدر:
Calculus, 2nd ed., Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra. Waltham, MA: Blaisdell
الجزء والصفحة:
...
29-9-2018
2381
Rolle's Theorem
Let 
be differentiable on the open interval 
and continuous on the closed interval ![[a,b]](http://mathworld.wolfram.com/images/equations/RollesTheorem/Inline3.gif)
. Then if 
, then there is at least one point 
where 
.
Note that in elementary texts, the additional (but superfluous) condition 
is sometimes added (e.g., Anton 1999, p. 260).
REFERENCES:
Anton, H. "Rolle's Theorem; Mean Value Theorem." §4.9 in Calculus: A New Horizon, 6th ed. New York: Wiley, pp. 260-266, 1999.
Apostol, T. M. Calculus, 2nd ed., Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra. Waltham, MA: Blaisdell, p. 184, 1967.
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