Casio fx-9750G Differential/Quadratic Differential, Inte Instrukcja Użytkownika Pobierz pdf (Strona 5)

3-3 Differential Calculations

• To perform differential calculations, first display the function analysis menu, and

then input the values shown in the formula below.

2(d/dx) f(x),a,∆x)

The differentiation for this type of calculation is defined as:

In this definition,

infinitesimal

is replaced by a

sufficiently small

∆x, with the value in

the neighborhood of f ' (a) calculated as:

In order to provide the best precision possible, this unit employs central difference to

perform differential calculations. The following illustrates central difference.

The slopes of point a and point a + ∆x, and of point a and point a – ∆x in function

y = f(x) are as follows:

In the above, ∆

y/∆x is called the forward difference, while ∇y/∇x is the backward

difference.To calculate derivatives, the unit takes the average between the value of

∆y/∆x and ∇y/∇x, thereby providing higher precision for derivatives.

P.64

Increase/decrease of

Point for which you want to determine the derivative

d/dx ( f (x), a, ∆x) ⇒ ––– f (a)

f (a + ∆x) – f (a)

f '(a) = lim –––––––––––––

∆x∆x→0

f (a + ∆x) – f (a) ∆y f (a) – f (a – ∆x) ∇y

––––––––––––– = ––– , ––––––––––––– = –––

∆x ∆x ∆x ∇x

f (a + ∆x) – f (a)

f '(a)

–––––––––––––

∆x

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Casio fx-9750G Differential/Quadratic Differential, Inte Instrukcja Użytkownika Strona 5