Finding All Critical Points of f(x,y)

**jegues** · November 6th 2010, 09:52 AM

I'm having some trouble finding all the critical points of the following function.

See figure attached for function and my work.

How can I get the equation of the line that contains all those critical points?

Thanks again!

**harish21** · November 6th 2010, 10:37 AM

the first and second lines of your solution should be:

$f_{x} = 3x^2y^3 - 2xy^2 = xy^2(3xy-2)$

and $f_{y}=3x^3y^2-2x^2y=x^2y(3xy-2)$

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