Casio fx-CG20 kSecond Derivative Calculations, Second Derivative Calculation Precautions, Using Second Derivative Calculation in a Graph Function, f ''(a), Example

kSecond Derivative Calculations [OPTN]-[CALC]-[d2/dx2]

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

<Math input/output mode>

K4(CALC)3(d2/dx2) f(x)ea

or

4(MATH)5(d2/dx2) f(x)ea

<Linear input/output mode>

K4(CALC)3(d2/dx2) f(x),a)

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

d2	d2
––– ( f (x), a) ⇒	––– f(a)
dx2	dx2

Second derivative calculations produce an approximate derivative value using the following second derivative formula, which is based on Newton’s polynomial interpretation.

f ''(a) =

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)

180h2

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 = x3 + 4x2 + x – 6

Input the function f(x).

AK4(CALC)3(d2/dx2)vMde+evx+v-ge

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

dw

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 = d2/dx2 (Y1). In this case, the value of the X variable is used instead of the value a.

Second Derivative Calculation Precautions

The precautions that apply for first derivative also apply when using a second derivative calculation (see page 2-28).

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