120
The meaning of messages
On pages 115, the values used were V=
27 78
,
U=16 67⋅ and D=100 and we were solving for A.
Thus:
22
2vu ad=−
became:
(
(
22
27 78 16 67 2 100 0a⋅−⋅+××= when substituted.
‘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’ - also indicates a correct solution, since normally one
expects to find an answer of zero at the point where the 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, such as that of a reciprocal graph at x = 0, but is more likely to
indicate a satisfactory answer.
The only time that you need to worry is when you receive any of the error
messages. These are:
‘Extremum’ - it found a minimum, but could not reach zero. Try solving
the equation
()
2
240x −+= and you will see this. The smallest
value that
()
2
240x −+= can have is 4 at x = 2, so the answer
supplied will be very close to this (such as 2.000000001 or
1.999999999). The problem is that unless you check
you may not realize that this is not actually a valid solution.
Calculator Tip
It is critical that students recognize this case since it occurs
quite often when the two sides of the equation (left and
right) come close but do not match. The student must
recognize that the answer is invalid and, preferably, why.
This is a major reason why it is often better to work in
the Function aplet, since it allows you to see clearly
whether or not there is a 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).
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