Critical Points of f(x,y)= x^{3} - 6xy + y^{3}

[jegues]

Homework Statement

Find and classify all critical points of,

f(x,y)= x^{3} - 6xy + y^{3}

Homework Equations

The Attempt at a Solution

See figure attached for my attempt at the solving all the critical points. I'm getting some weird numbers so I want to make sure I did this part correct before I start classifying them.

Does anyone see any problems?

Thanks again!

 

[tiny-tim]

hi jegues!

in line 6, your 1/8 should be 1/4

(btw, it would be a lot easier if you divided everything by 3 first)

 

[JeSuisConf]

You can quickly check your work using wolfram alpha... and according to it, (0,0) is one but your other answers are wrong.