Show-that-the-surface-z-xy-has-neither-a-maximum-nor-a-minimum-point-

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

Show that the surface

z = xy

has neither a maximum nor a minimum point

Commented by AST last updated on 30/Jan/24

F o r x, y \to \infty; z \to \infty

F o r x \to \infty; y \to - \infty \Rightarrow z \to - \infty

Commented by Mastermind last updated on 30/Jan/24

I need full detail, using pdf test

Commented by AST last updated on 30/Jan/24

\frac{\partial z}{\partial y} = x; \frac{\partial z}{\partial x} = y \dots E q u a t i n g t o 0 \Rightarrow (x, y) = (0, 0)

Y o u a l s o h a v e t o c h e c k b o u n d a r y p o i n t s, w h i c h

i s w h a t i s u p t h e r e . P a r t i a l d i f f e r e n t i a l s d o n o t

g i v e a l l c r i t i c a l p o i n t s .

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