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Question Number 203859 by Mastermind last updated on 30/Jan/24

$$\mathrm{Show}\mathrm{that}\mathrm{the}\mathrm{surface}$$$$\mathrm{z}=\mathrm{xy}$$$$\mathrm{has}\mathrm{neither}\mathrm{a}\mathrm{maximum}\mathrm{nor}\mathrm{a}\mathrm{minimum}\mathrm{point}$$

Commented by deleteduser1 last updated on 30/Jan/24

$$Forx,y\to \mathrm{\infty };z\to \mathrm{\infty }$$$$Forx\to \mathrm{\infty };y\to -\mathrm{\infty }\Rightarrow z\to -\mathrm{\infty }$$

Commented by Mastermind last updated on 30/Jan/24

$$\mathrm{I}\mathrm{need}\mathrm{full}\mathrm{detail},\mathrm{using}\mathrm{pdf}\mathrm{test}$$

Commented by deleteduser1 last updated on 30/Jan/24

$$\frac{\partial z}{\partial y}=x;\frac{\partial z}{\partial x}=y...Equatingto0\Rightarrow (x,y)=(0,0)$$$$Youalsohavetocheckboundarypoints,which$$$$iswhatisupthere.Partialdifferentialsdonot$$$$giveallcriticalpoints.$$

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