Lagrange's Theorem If a function f(x) is continuous in the closed interval [a, b] and is differentiable in the open interval (a,b), then there exists at least one c belongs (a, b) such that f(b) – f(a) f'(c) = b - a

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 42E
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Use Frobenius's theorem to  proof of Lagrange's theorem.

Lagrange's Theorem
If a function f(æ) is continuous in the closed
interval [a, b] and is differentiable in the open
interval (a,b), then there exists at least one c
belongs (a, b) such that
f(b) – f(a)
b - a
-
f' (c) =
Transcribed Image Text:Lagrange's Theorem If a function f(æ) is continuous in the closed interval [a, b] and is differentiable in the open interval (a,b), then there exists at least one c belongs (a, b) such that f(b) – f(a) b - a - f' (c) =
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