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 – 2
x
) and the width is (4 – 2
x
). The volume
V
is
given by
V
= (8 – 2
x
)(4 – 2
x
)
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.
6
002– 6
Assumes stack loaded with
x.
Summary of Contents for HP-15C
Page 1: ...HP 15C Owner s Handbook HP Part Number 00015 90001 Edition 2 4 Sep 2011 ...
Page 17: ...Part l HP 15C Fundamentals ...
Page 64: ......
Page 65: ...Part ll HP 15C Programming ...
Page 118: ...118 ...
