•Inaccurate results and errors can be caused by the following:

-discontinuous points in x values

-extreme changes in x values

-inclusion of the local maximum point and local minimum point in x values

-inclusion of the inflection point in x values

-inclusion of undifferentiable points in x values

-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, 3, maximum/minimum value, Solve, RndFix or logab calculation expression inside a differential calculation term.

•In the Math input/output mode, the tolerance value is fixed at 1E–10 and cannot be changed.

IQuadratic Differential Calculations

[OPTN]-[CALC]-[d2/dx2]

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

*(CALC)*(d2/dx2) f(x) a tol

* fx-7400GII: (CALC)

(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).

*(CALC)* (d2/dx2) T,BCTVT E

* fx-7400GII: (CALC)

Input 3 as point a, which is the differential coefficient point.

B

Input the tolerance value.

@$ D

U

Quadratic Differential Calculation Precautions

•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.

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