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

  • Dennis M. CatesEmail author
Chapter

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 power 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 homogeneous function of \( x, y, z, \dots \) and of degree a,  if, t denoting a new variable, we have regardless of t, .
$$\begin{aligned} f(tx, ty, tz, \dots )=t^af(x, y, z, \dots ). \end{aligned}$$
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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Sun CityUSA

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