HP 39gs Master Manual page 107

Multiple solutions and the initial guess
Our first example was fairly simple because there was only one solution so it did not much matter where we
began looking for it. When there is more than one possible answer you are required to supply an initial
estimate or guess. The Solve aplet will then try to find a solution which is 'near' to the estimate.
Example 1
The volume of a cylinder is given by V = 2 π r r h
cylinder which has a volume of 1 liter and a height of 10cm.
Enter the equation into
E1
equation, ensure that you put a * sign between the
See page 79 for more information on the reason for this.
Change to the view and enter the known values, remembering that
NUM
1 liter=1000cm 3 . Position the highlight over
your estimate, and press
8.57cm. The equation is a quadratic in
are possible. If you enter an initial estimate of -10 you will obtain the
negative solution, which is physically invalid in this case.
Example 2
( )
If f x = x − 2x − 5x + 2 find all values of x for which f x
3 2
Although you may have a clear picture in your mind and can provide Solve with the estimates it needs, I'll
assume that, like me, you would find it helpful to see a graph first.
It is also possible to solve this in the Function aplet, which offers more
powerful tools. The
PLOT
can be deceptive if you don't understand it and I sometimes find it easier
to work in the Function aplet. In this case we will continue to work in
Solve.
Graphing in Solve
In the view, enter the equation
SYMB
view, enter the known value of
NUM
, making it the active variable, and then press
X
does not look like this then you may not have had the highlight on the
or your axes may not be set the same as mine in
as shown right. When you are entering the
, enter a positive value as
R
to find the solution shown right of
which means two solutions
R
view in the Solve aplet, although powerful,
2
Y=X^3-2X
, ensure that the highlight is on
Y=1
PLOT
PLOT SETUP
( )
. Find the radius of a
+
and the bracket.
R
( )
= 1 .
into . In the
-5X+2 E1
. If your view
,
X
.
107