4 quadratic differential calculations – Casio fx-9750G Differential/Quadratic Differential, Integration, Value User Manual
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3-4 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 polyno-
mial interpretation.
–
f(x – 2h) + 16 f (x – h) – 30 f(x) + 16 f(x + h) – f(x + 2h)
f''(x)
=
–––––––––––––––––––––––––––––––––––––––––––––––
12h
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
calcu-
lated 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.
uuuuu
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
K4
(CALC)
3
(
d
2
/
dx
2
)
v
Md+evx+
v-g,
P.64
d
2
d
2
–––
( f (x), a, n)
⇒
–––
f (a)
dx
2
dx
2
Final boundary (
n
= 1 to 15)
Differential coefficient point
1 2
3
4 5 6