Casio fx-9750G PLUS - Manual (Page 86)

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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 – 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
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 K4 (CALC)3( d 2 / dx 2 ) vMd+
evx+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