你也一样的英文What is the definition of the derivative

2021年1月19日发(作者：震动)
What is the definition of the
derivative?

Example:

An
acquisition
officer
observed
the
cost
of
similar
defense
contracts
for
the
past
10
years.
He
is
interested
in
the
rate
of
change
in
the
costs
for contracts
that
last
2
years.
The
following table depicts the values he obtained.

Duration in months Cost in $$1,000
10
20
30
40
50
60
33
79
165
236
362
491

Using these values, he plotted the points on a graph
of
COST
versus
DURATION
as represented by the
red dots
in
the illustration below
.



COST

DURATION
Please
refer
to
the
graphing
functions
station
for
methods
for deriving a function from a graph.
From
the
graph,
he
was
able
to
find
a
function
(illustrated
by the
blue line
, above) which represents the graph
of
cost c
versus
time t
. The officer found that the
function which best fits the points on the graph is

c = 0.1 t
+ 2t


2
With
this
function,
he
was
able
to
compute
the
rate
of
change
in cost with respect to duration by using the concept
of
derivatives
. The acquisition officer took the
derivative
c'
of the function
c

c' = 0.2 t + 2


With the derivative
c'
, he can now determine the rate of
change
of
cost
of
a
contract
as
it
increases
beyond
two
years
or
24
months.
The
derivative
c'
at
time
t
=
24
months
given
in $$1000's per month is then

c' = 0.2 × 24 + 2 = 2.48



Definition:

What
is
this
derivative
and
how
does
it
work?
Let
us
see
what
the
definition of derivative is. A derivative
f'(x)
of a
function
f
depicts
how
the
function
f
is
changing
at
point
x
.
It
is necessary for the function
f
to be
continuous
at point
x
in
order
for
there
to
be
a
derivative
at
that
point.
A
function
which
has a derivative is said to be
differentiable
.
The derivative is computed by using the concept of
x
.
x
is an
arbitrary
change
or
increment
in
the
value
of
x
.
You
can
see
that
if
x
in
the
example
above
is
10
months,
you
can
readily
compute
the
rate
of
change
in
the
function,
but
the
officer
wanted
to
know
the
rate
of
change
at
a
particular
point
x
,
not
a
span
of
10
months.
The derivative is the limit approached by the rate of change in
the function when
x
becomes arbitrarily small.