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Calculus: Differentiation and Integration, 1st Edition
book

Calculus: Differentiation and Integration, 1st Edition

by ICFAI
April 2024
Intermediate to advanced content levelIntermediate to advanced
710 pages
20h 50m
English
Pearson India
Content preview from Calculus: Differentiation and Integration, 1st Edition
Mean Value Theorems 9-11
Hence by mean value theorem, there exists c Î (a, b) such that
f ' c
f b f a
b a b a
( )
( ) ( )
.=
=
=
0 0
0
Therefore, f ′(x) = 0 has a root x = c.
Note 9.2 In this example, f can have more than one root.
9.3 CAUCHY’S MEAN VALUE THEOREM
Cauchy’s mean value theorem, which is also known as the second mean value theorem or extended
mean value theorem, is the more general form of the mean value theorem and it deals with two
functions f and F.
STATEMENT If two functions f and F are:
a. Both continuous in [a, b]
b. Both differentiable in (a, b)
c. F′(x) ¹ 0 for any x Î (a, b), then there exists at least one real ...
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Publisher Resources

ISBN: 9789353948221