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For ax²+bx+c functions :

Download :

Edited: 13 Aug 2012, 12:45 p.m.


Expliquez, s.v.p. En anglais préférablement. Merci.

Pour quoi?

I posted in english, no ?
Just the screenshot is in french.

'Tableau de variation' in french, is a table representative of the sign of the derivative of a function. It is used, usually for analyzing a function prior to its plotting 'by hand'.
The table shows segments on which the function is constantly increasing or decreasing, which is directly related with the sign of the derivative.
In that particular case it seems to be handling 2nd degrees polynomials.


Thanks for the explanation. It's an idea I hadn't heard of before.

Thank you for your explanation :-)

Nevertheless, on a calculator which allows for graphing the function or its derivative itself I hesitate to see much value in such a "variation table" just telling me there's something anywhere in between -infinity and +infinity. I dare say I'd guessed that [;-) but presumably I missed something essential.

The command TABVAR in the 48 series does just this. Doesn't actually plot, but has a nice numerical only table identifying all the important bits of the function and the behavior in the various.


Not in the entire series, however.

Well, it is a bit of historical interest now. But before graphing calculators were widely spread among students it was a very 'popular' exercise in math teaching for 'analyzing a function'. The game was to plot the function by hand. There is a kind of systematic method which was teach intensely to math students. And it is a very concrete and immediate application of the notion of derivative.
Lot of stupid conclusions have been avoided by building a 'table of variations'.

Beside history, it is of interest for functions with discontinuities where graphing algorithms can fail and for getting a firm understanding of a function.

Sometimes it is amazing what you can do with a paper and a pencil, even without an HP calculator....;-)

Hmm. Thought was introduced on the S. Must have been the G then.


For example the 'variation table' of X^2+3*X+1

In just one glance, you see the essential

On 50G, it's

'X^2+3*X+1' TABVAR

Table is useful to study the signs of the derivative and to draw with precision the graph.
In France, students learn to study functions like this.
I don't know if it is historical or practical but it is a real competence asked in exams (question like "Give the table of variation of the function.").

I said it was a bit historical because french students, as the others...jump first on their calculator, then think about the strange plot they get and finally try to get a table of variation with the very same calculator if possible. ;-) Turning the brain on before the calculator is a vanishing habit those days....
I confess that if I have had a graphing calculator at the time I was a student I would probably have done the same asking why I should have suffer in tedious calculations while it was so simple to push some keys....


I think that you need to install Erable 3.2 on the 48G/GX to get TABVAR.

Well, I guess I was completely wrong on all counts. I was certain I used it on my first HP - a 48G. I know I didn't install anything fancy on it. That was in 1997 or so though, so I must be getting old as my memory is failing. :-)