Casio CFX-9850G PLUS, User'S Manual & Technical Reference

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58
3-3 Quadratic Differential Calculations
After displaying the function analysis menu, you can input quadratic differentials
using either of the two following formats.
3
(
d
2 /
dx
2
)
f ( x )
,
a
,
n
)
Quadratic differential calculations produce an approximate differential value using
the following second order differential formula, which is based on Newton's
polynomial interpretation.
–
f ( x – 2 h ) + 16 f ( x – h ) – 30 f ( x ) + 16 f ( x + h ) – f ( x + 2 h )
f'' ( x )
=
–––––––––––––––––––––––––––––––––––––––––––––––
12 h
2
In this expression, values for “sufficiently small increments of
x
” are sequentially
calculated using the following formula, with the value of
m
being substituted as
m
= 1, 2, 3 and so on.
1
h = ––––
5
m
The calculation is finished when the value of
f " ( x )
based on the value of
h
calculated using the last value of m , and the value of f "
(
x
)
based on the value of
h
calculated using the current value of
m
are identical before the upper
n
digit is
reached.
• Normally, you should not input a value for
n
. It is recommended that you only
input a value for
n
when required for calculation precision.
• Inputting a larger value for
n
does not necessarily produce greater precision.
u u u u u
To perform a quadratic differential calculation
Example To determine the quadratic differential coefficient at the point
where
x
= 3 for the function
y
=
x
3 +
4
x
2 +
x
– 6
Here we will use a final boundary value of
n
= 6.
Input the function
f
(
x
) .
A K 4
(CALC)
3
(
d
2
/
dx
2
)
v M d+
e vx + v -g,
[OPTN] - [CALC] - [
d 2
/
dx 2
]
d
2
d
2
–––
( f ( x ), a , n )
⇒
–––
f ( a )
dx
2
dx
2
Final boundary (
n
= 1 to 15)
Differential coefficient point