Quadratic Differential Calculations - Casio fx-9750GII User Manual

• Inaccurate results and errors can be caused by the following:
- discontinuous points in
- extreme changes in
- inclusion of the local maximum point and local minimum point in
- inclusion of the inflection point in
- inclusion of undifferentiable points in
- differential calculation results approaching zero
• Always use radians (Rad mode) as the angle unit when performing trigonometric differentials.
• You cannot use a differential, quadratic differential, integration, , maximum/minimum value,
Solve, RndFix or log
• In the Math input/output mode, the tolerance value is fixed at 1

Quadratic Differential Calculations

After displaying the function analysis menu, you can input quadratic differentials using the
following syntax.
(CALC)*
a
( : differential coefficient point,
2 2
d d
––– ( f (x), a) ––– ( f (x), a)
2 2
dx dx
Quadratic differential calculations produce an approximate differential value using the following
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) 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) f ''(a)
= =
In this expression, values for "sufficiently small increments of
f " a
approximates (
Example
Input the function
a
Input 3 as point
Input the tolerance value.
Quadratic Differential Calculation Precautions
f
• In the function
through Z excluding X,
that variable is applied during the calculation.
x
values
x
values
x
b calculation expression inside a differential calculation term.
a
d dx f x a
2 2
( / ) ( )
tol
2 2
d d
––– f (a) ––– f (a)
2 2
dx dx
).
To determine the quadratic differential coefficient at the point where
x
= 3 for the function
Here we will use a tolerance
f x
( ).
(CALC)*
, which is the differential coefficient point.
x
( ), only X can be used as a variable in expressions. Other variables (A
r
, ) are treated as constants, and the value currently assigned to
values
x
values
tol
: tolerance)
2 2
180h 180h
y x 3 x 2 x
= + 4 + – 6
tol
= 1 – 5
E
d dx
( 2 / 2 )
2-25
x
values
–10 and cannot be changed.
E
[OPTN]-[CALC]-[
II
* fx-7400G
h
" are used to obtain a value that
II
* fx-7400G
2 / 2
d dx
]
: (CALC)
: (CALC)