HP -32S Owner's Manual page 125

LIE
HE
15.0000
0.0000
This value from the Y-
regjster is the estimate
made just prior to the
final result. Since it is
the same as the solu
tion, the solution is an
exact root...
...and, as this value
from the Z-register
shows, f(x) = 0 at the
root.
The dimensions of the desired box are 50 x 10 x 15 cm. If you
ignored the upper limit on the height (20 cm) and used initial esti
mates of 30 and 40 cm, you would obtain a height of 42.0256 cm—a
root that is physically meaningless. If you used small initial estimates
such as 0 and 10 cm, you would obtain a height of 2.9744 cm—pro
ducing an undesirably short, flat box.
Using Graphs to Select Initial Guesses. As an aid to understand
ing the behavior of a particular function, you can graph it. Use your
program routine to evaluate the function for several values of the un
known. For each point on the graph, store the value for the x-
coordinate in the variable, and then obtain the corresponding value for
the y-coordinate by pressing Ixeqi label. For the problem above, you
would always set V* = 7500 and vary the value of H to produce dif
ferent values for the function. The plot of this function looks like this:
iff C40-#) C20-#) -7500
i
• 30.000
-20.000
x-H
7: Solving ffor an Unknown Variable in an Equation 123