⋅
⋅
The meaning of
messages
On pages 106, the values used were
V=
27 78
,
U=
16 67
and
D=
100
and we were solving for
A
.
2
2
Thus:
v
=
u
+
2
ad
2
2
⋅
⋅
2
a
=
became:
(
27 78
)
−
(
16 67
)
− × ×
100 0
when substituted and re-arranged.
When you press
there are a number of possible positive responses. They are:
•
Zero
- The calculator tried to find a value of
A
which made this zero and, in the
message
shown above, it is reporting that it succeeded.
•
Sign reversal
- This also indicates a correct solution, since normally one expects to find an
answer of zero at a point where the re-arranged equation changes from positive to negative (or vice
versa). ‘Sign reversal’ is a report that it couldn’t get an answer to 12 significant digits that was
precisely zero, just two answers minutely on either side of zero. This might indicate a discontinuity at
the point but is more likely to indicate a satisfactory answer.
The only time that you need to worry is when you receive any of the messages below. These are:
2
•
Extremum
- it found a minimum, but could not reach zero. Try solving the equation
(
x
−
2
)
+
4
0
=
2
and you will see this. The smallest value that
(
x
−
2
)
+ =
can have is 4 at x=2, so the answer
4
0
unless you check
supplied will be very close to this (such as 2.000000001 or 1.999999999). The problem is that
you may not realize that this is not actually a valid solution.
•
Bad Guess
- the initial estimate you supplied was outside the domain of the function. For example,
the equation uses a square root or a logarithm and you began from a value involving a negative.
•
Constant?
- no solution was found. The value of the function was the same at every point tested
and wasn’t the value you wanted.
Calculator Tip
l
is invalid and, preferably, why.
It is critical that students recognize the
Extremum
case since it occurs
quite often when the two sides of the equation approach c osely but do
not quite intersect. The student must at least recognize that the answer
This is the major reason why it is generally better to work
in the Function aplet, since it allows you to see clearly
whether or not there is a solution.
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