115
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
)
2Vrrh
π
+ . Find the radius of a
cylinder which has a volume of 1 liter and a height of 10cm.
Enter the equation into E1 as shown right.
When you are entering the equation, ensure
that you put a * sign between the R and the
bracket. See page 87 for more information on
this.
Change to the NUM view and enter the known
values, remembering that 1 liter=1000cm
3
.
Position the highlight over R, enter a positive
value as your estimate, and press to
find the solution shown right of 8.57cm. The
equation is a quadratic in R which means two
solutions 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
()
32
252fx x x x=− −+
find all values of x for which
)
1fx
.
Although you may have a clear picture in your mind and can provide Solve
with the estimates it needs, I’ll assume that 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 view in the Solve aplet, although
powerful, 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.
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