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Question Number 182797 by universe last updated on 14/Dec/22
 find  the max and  min value   f(x,y,z) = x^3 +y^3 +z^3 −9xy−9xz+27x
$$\:\mathrm{find}\:\:\mathrm{the}\:\mathrm{max}\:\mathrm{and}\:\:\mathrm{min}\:\mathrm{value} \\ $$$$\:\mathrm{f}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\:=\:\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} +\mathrm{z}^{\mathrm{3}} −\mathrm{9xy}−\mathrm{9xz}+\mathrm{27x} \\ $$
Commented by mahdipoor last updated on 14/Dec/22
±∞  get  x=y=z ⇒f=3x^3 −18x^2 +27x  min and max f=±∞
$$\pm\infty \\ $$$${get}\:\:{x}={y}={z}\:\Rightarrow{f}=\mathrm{3}{x}^{\mathrm{3}} −\mathrm{18}{x}^{\mathrm{2}} +\mathrm{27}{x} \\ $$$${min}\:{and}\:{max}\:{f}=\pm\infty \\ $$

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