Casio ALGEBRA FX 2.0 Manual Calculations - Manual (Page 32)

19990401
k k k k k Quadratic Differential Calculations
[OPTN]-[CALC]-[d 2 /dx 2 ]
After displaying the function analysis menu, you can input quadratic differentials using either of
the two following formats.
K4(CALC)c( d 2 / dx 2 ) f(x) , a ,tol)
Quadratic differential calculations produce an approximate differential value using the follow-
ing second order differential formula, which is based on Newton's polynomial interpretation.
2 f(a + 3h) – 27 f(a + 2h) + 270 f (a + h) – 490 f(a)+270 f(a – h) – 27 f(a – 2h) +2 f(a – 3h)
f ''(a) = –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––
180h 2
In this expression, values for “sufficiently small increments of h” are used to obtain a value that
approximates f ”(a).
○ ○ ○ ○ ○
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 tolerance tol = 1
E
– 5
Input the function f( x ).
AK4(CALC)c( d 2 / dx 2 ) v Md+
e vx+v-g,
Input 3 as point a , which is differential coefficient point.
d,
Input the tolerance value.
b E-f)
w
2-5-5
Numerical Calculations
# In the function f(x), only X can be used as a
variable in expressions. Other variables (A
through Z, r,
θ ) are treated as constants, and
the value currently assigned to that variable is
applied during the calculation.
# Input of the tolerance (tol) value and the closing
parenthesis can be omitted.
# Discontinuous points or sections with drastic
fluctuation can adversely affect precision or
even cause an error.
( a : differential coefficient point , tol: tolerance)
d 2 d 2
––– (f (x), a) ⇒ ––– f (a)
dx 2 dx 2