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Numerical Calculations

kQuadratic Differential Calculations[OPTN]-[CALC]-[d2/dx2]

After displaying the function analysis menu, you can input quadratic differentials using the following syntax.

K4(CALC)3(d2/dx2) f(x),a,tol)(a: differential coefficient point, tol: tolerance)

d2

⇒

d2

––– ( f (x), a)––– f(a)
dx2

 

dx2

Quadratic differential calculations produce an approximate differential value using the following second order differential 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 quadratic differential coefficient at the point where

 

x = 3 for the function y = x3 + 4x2 + x – 6

 

Here we will use a tolerance tol = 1E – 5

Input the function f(x).

AK4(CALC)3(d2/dx2) vMd+evx+v-g,Input 3 as point a, which is the differential coefficient point.

d,

Input the tolerance value.

bE-f)

w

#In the function f(x), only X can be used as a variable in expressions. Other variables (A through Z excluding X, r, Ƨ) 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.

#Specify a tolerance (tol) value of 1E-14 or greater. An error (Time Out) occurs whenever no solution that satisfies the tolerance value can be obtained.

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