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Higher degree derivatives.
Definition
6
.
10
.
1
Let
be a function, differentiable on an neighborhood of
. If
is differentiable at
, its first derivative
is called the
the second derivative
of
at
. By induction we define the
derivative of a function at a point
; we denote it by
.
Example
6
.
10
.
2
Take
. Then, for every
, we have:
Example
6
.
10
.
3
If
, then for every
, we have:
If
, then for every
.
If
, then we have:
(Check this by induction!)
Example
6
.
10
.
4
Let
be the function defined by
Subsections
Convexity and concavity of a function.
Application to finding extremal points.
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Convexity and concavity of
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Differentiable functions.
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Noah Dana-Picard 2007-12-28