March 2014
Intermediate to advanced
412 pages
11h 16m
English
Content preview from Numerical Methods and Optimization
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28 Numerical Methods and Optimization: An Introduction
at x
0
if there exists the limit f
(x
0
) = lim
x→x
0
f(x)−f(x
0
)
x−x
0
, in which case f
(x
0
)
is called the first-order derivative,orsimplythederivative of f at x
0
.Iff is
differentiable at x
0
, then it is continuous at x
0
. The opposite is not true in
general; in fact, there exist continuous functions that are not differentiable at
any point of their domain. If f is continuous (differentiable) at every point of
X,thenf is called continuous (differentiable) on X. The set of all continuous
functions on X is denoted by C(X). The k
th
order derivative f
(k)
(x
0
)off
at x
0
can be defined recursively as the first-order deriv ...
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