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Real Analysis
book

Real Analysis

by V. Karunakaran
May 2024
Intermediate to advanced content levelIntermediate to advanced
585 pages
15h 38m
English
Pearson India
Content preview from Real Analysis
“real: chapter_06” 2011/5/22 23:14 page9—#9
Differentiation 6-9
Hence
g
(y) =
1
sec
2
x
=
1
1 + tan
2
x
=
1
1 + y
2
.
6.3 LOCAL EXTREMA AND MEAN VALUE THEOREMS
Definition 6.3.1 Let S R and f : S R be a function. We say that
f has a local maximum at a S if there exists a neighbourhood U of
a such that for all x U S, f (x) f (a). If on the other hand under
the same conditions f (x) f (a) for all x U S, then we say that f
has a local minimum at a.
Theorem 6.3.2 Let S be an interval and f : S
R be differentiable
at a S.
(i) If f has a local maximum at x = a and a is not the left end point
of S, then f
(a) 0.
(ii) If f has a local minimum at x = ...
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Publisher Resources

ISBN: 9781299447561Publisher Website