Sign table

A sign table is in the mathematics one a method inequality to solve or the sign of a function to be determined and presented in tabular form.

application

The sign table is based on the fact that the sign of a product or a quotient can be determined from the individual factors: the multiplication or division of two factors with the same sign results in a positive term; if the signs are different, the result is a negative term. An inequality can be solved by evaluating the function on which the corresponding equation is based.

In France , the use of the sign table ( French tableau de signes ) is an integral part of the grammar school mathematics program.

In the sign table, the individual factors of the function to be evaluated are displayed line by line. In each line, its sign is shown depending on the values ​​of the variable, with zeros being indicated by a solid vertical line. Values ​​outside the definition range are marked with a vertical double line.

Furthermore, after evaluating the sign of the derivative, the course of a function ( monotonically rising or falling) and the local extreme values ​​are graphically displayed in the sign table.

example

The inequality that is defined for is to be solved . ${\displaystyle {\frac {1}{x^{2}}}\leq {\frac {1}{2-x}}}$ ${\displaystyle x\in \mathbb {R} \backslash \{0,2\}}$

This inequality can be transformed step by step as follows:

${\displaystyle {\begin{aligned}&{\frac {1}{x^{2}}}-{\frac {1}{2-x}}\leq 0\\\Leftrightarrow \quad &{\frac {-x^{2}-x+2}{x^{2}(2-x)}}\leq 0\\\Leftrightarrow \quad &{\frac {(-x+1)(x+2)}{x^{2}(2-x)}}\leq 0\end{aligned}}}$

By entering the four factors in a sign table, the sign of the left side of the inequality can be determined:

The solution set of the inequality is thus . ${\displaystyle L={]{-\infty },-2]}\cup [1,2[}$

literature

• Hoffmann Di Marzio et al: Mathematics for technical colleges, technical schools - technical subject area, p. 64 ff. Bildungsverlag Eins, Troisdorf 2007, ISBN 3-427-21521-0

Web links

• Comprendre les maths, cours de seconde: Tableaux de signes (French)

Individual proof

1. ↑ Bulletin Officiel du ministère de l'Education Nationale et du ministère de la Recherche 2001-156 du 7-8-2001 ( PDF, 100 KB  ( page no longer available , search in web archives )  Info: The link was automatically marked as defective. Please check the link according to the instructions and then remove this notice. )