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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
4-6  Calculus – Differentiation and Integration
CONVERSE
The converse of the theorem is false. That is, a continuous function need not be differentiable.
Example: Consider the function f(x) = |x|. We know that f is continuous at 0.
But f is not differentiable at 0 because
f '
x h x
h
x h x
h
h
h
( ) lim
lim
0
1
0
0
+
=
+
=
+
=
+
+
and
f '
x h x
h
x h x
h
f ' f '
h
h
( ) lim
lim
( )
.
( ) ( ).
0
1
0 0
0
0
+
=
+
=
+
=
+
4.1.1 Derivative as the Rate of Change
The concept of derivative can also be described as a method to compute the rate at which a
dependent output y changes with respect to the change in the independent input x. This rat
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Publisher Resources

ISBN: 9789353948221