Casio FX-CG10 Manual do Utilizador descarregar pdf (Página 75)

100

101

2-29

k Second Derivative Calculations [OPTN] - [CALC] - [ d

/ dx

]

After displaying the function analysis menu, you can input second derivatives using the

following syntax.

K4(CALC)3(d

/dx

) f(x)ea

4(MATH)5(d

/dx

) f(x)ea

K4(CALC) 3( d

/ dx

) f ( x ) ,a )

a is the point for which you want to determine the second derivative.

Second derivative calculations produce an approximate derivative value using the following

second derivative formula, which is based on Newton’s polynomial interpretation.

In this expression, values for “sufficiently small increments of

h ” are used to obtain a value that

approximates f

( a ).

Example To determine the second derivative at

x = 3 for the function

y = x

+ 4 x

+ x – 6

Input the function f ( x ).

AK4(CALC) 3( d

/ dx

) vMde+evx+v-ge

Input 3 as point a , which is the derivative point.

Using Second Derivative Calculation in a Graph Function

You can omit input of the value a in the syntax above by using the following format for the

second derivative graph: Y2 = d

/dx

(Y1). In this case, the value of the X variable is used

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 2-28).

––– (

(

)

⇒

–––

(

)

––– (

(

)

⇒

–––

(

)

''(a) =

180h

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)

''(a) =

180h

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)

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