- #1

knowlewj01

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## Homework Statement

Find the critical points of this function and determine wether they are local maxima, minima or saddle points...

[itex]f=\frac{1}{x} + \frac{1}{y} + xy[/itex]

## The Attempt at a Solution

start off by partially differentiating and setting to zero for x and y:

[itex] \frac{\partial f}{\partial x}=\frac{\partial f}{\partial y}=0[/itex]

[itex]\frac{\partial f}{\partial x}= -\frac{1}{x^2} + y = 0[/itex]

[itex]\therefore y=\frac{1}{x^2}[/itex]

[itex]\frac{\partial f}{\partial y}= -\frac{1}{y^2} + x = 0[/itex]

[itex]\therefore x=\frac{1}{y^2}[/itex]

so:

[itex]\exists[/itex] a stationary point at [itex](\frac{1}{y^2},\frac{1}{x^2})[/itex]

using [itex] D = f_{xx}f_{yy} - (f_{xy})^2[/itex]

Does all of this look ok so far? because i do not get a definitive answer for where the critical point lies or any indication of it's nature.