Geodesic
Quadratic functions in several variables
The Teaching of Mathematics, VIII (2005) no. 2, p. 53 .

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In secondary schools students learn to investigate the behavior of the quadratic function in one variable, and to find the point where the function reaches its extremal value. The purpose of this article is to demonstrate how the idea which is applied to functions in one variable can be extended and applied to functions in several variables. We present the procedure to determine whether a quadratic function in several variables has a minimum or a maximum, and if it has, to find points in which the extremal value is reached. This procedure leads to several theoretical results.
Classification : 00A35 I65
Keywords: quadratic functions in several variables, quadratic forms, extremal values, definitness, Sylvester Criterion 
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     author = {Vladimir Jankovi\'c},
     title = {Quadratic functions in several variables},
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Vladimir Janković. Quadratic functions in several variables. The Teaching of Mathematics, VIII (2005) no. 2, p. 53 . http://geodesic.mathdoc.fr/item/TM2_2005_VIII_2_a0/