THEOREM OF HOMOGENEOUS FUNCTIONS. MAXIMA AND MINIMA OF FUNCTIONS OF SEVERAL VARIABLES

Dennis M. Cates ()

Chapter Chapter 10 in Cauchy's Calcul Infinitésimal, 2019, pp 49-52 from Springer

Abstract: Abstract We say that a function of several variables is homogeneous, when, by letting all of the variables grow or decline in a given ratio, we obtain for a result the original value of the function multiplied by a powerHomogeneous function of this ratio. The exponent of this power is the degree of the homogeneous function. By consequence, $$f(x, y, z, \dots )$$ will be a homogeneousDegree of homogeneous function function of $$ x, y, z, \dots $$ and of degree a, if, t denoting a new variable, we have regardless of t, . $$\begin{aligned} f(tx, ty, tz, \dots )=t^af(x, y, z, \dots ). \end{aligned}$$ .

Date: 2019
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DOI: 10.1007/978-3-030-11036-9_10

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