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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

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