HP 15C Uživatelský manuál stáhnout pdf (Strana 189)

Section 13: Finding the Roots of an Equation 189

If you have some knowledge of the behavior of the function f(x) as it varies

with different values of x, you are in a position to specify initial estimates in

the general vicinity of a zero of the function. You can also avoid the more

troublesome ranges of x such as those producing a relatively constant

function value or a minimum of the function's magnitude.

Example: Using a rectangular piece

of sheet metal 4 decimeters by 8

decimeters, an open-top box having a

volume of 7.5 cubic decimeters is to

be formed. How should the metal be

folded? (A taller box is preferred to a

shorter one.)

Solution: You need to find the height

of the box (that is, the amount to be

folded up along each of the four sides)

that gives the specified volume. If x is

the height (or amount folded up), the

length of the box is (8  2x) and the width is (4  2x). The volume V is

given by

V = (8  2x)(4  2x) x.

By expanding the expression and then using Horner's method (page 79), this

equation can be rewritten as

V = 4 ((x  6) x + 8) x.

To get V= 7.5, find the values of x for which

f(x) = 4 ((x  6) x + 8) x  7.5 = 0.

The following subroutine calculates f(x):

Keystrokes

Display

| ¥

000–

Program mode.

´b 3

001–42,21, 3

Label.

002– 6

Assumes stack loaded with x.

1 2 ... 184 185 186 187 188 189 190 191 192 193 194 ... 287 288

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HP 15C Uživatelský manuál Strana 189