Second Derivative Calculations; Using Second Derivative Calculation In A Graph Function; Second Derivative Calculation Precautions - Casio FX-CG20 AU User Manual

k Second Derivative Calculations
After displaying the function analysis menu, you can input second derivatives using the
following syntax.
<Math input/output mode>
K4(CALC)3(d
or
4(MATH)5(d
<Linear input/output mode>
K4(CALC)3(d
a
is the point for which you want to determine the second derivative.
2 2
d d
––– ( f (x), a) ⇒ ––– f (a) ––– ( f (x), a) ⇒ ––– f (a)
2 2
dx dx
Second derivative calculations produce an approximate derivative value using the following
second derivative 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 "
approximates (
Example
Input the function
a
Input 3 as point

Using Second Derivative Calculation in a Graph Function

You can omit input of the value
second derivative graph: Y2 = d
instead of the value

Second Derivative Calculation Precautions

The precautions that apply for first derivative also apply when using a second derivative
calculation (see page 2-29).
2 x 2 f x a
/d ) ( )e
2 x 2 f x a
/d ) ( )e
x f x a )
2 2
/d ) ( ),
2 2
d d
2 2
dx dx
a
).
To determine the second derivative at
y x 3 x 2 x
= + 4 + – 6
f x
( ).
AK4(CALC)3(d
, which is the derivative point.
dw
a
in the syntax above by using the following format for the
2 x 2
/d (Y1). In this case, the value of the X variable is used
a
.
2 2
180h 180h
h
x
= 3 for the function
x
2 2
/d )vMde+evx+v-ge
2-30
[OPTN]-[CALC]-[d
" are used to obtain a value that
2 2
x
/d ]