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

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The discussion focuses on finding and classifying the critical points of the function f(x,y) = x^3 - 6xy + y^3. The original poster expresses uncertainty about their calculations, particularly regarding the critical points they identified. A participant points out a specific error in the calculations, suggesting that a value should be corrected from 1/8 to 1/4. Additionally, they recommend simplifying the equation by dividing by 3 and using Wolfram Alpha for verification. The critical point (0,0) is confirmed, but other identified points are deemed incorrect.
jegues
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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!
 

Attachments

  • 09Q7.jpg
    09Q7.jpg
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hi jegues! :smile:

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

(btw, it would be a lot easier if you divided everything by 3 first)
 
You can quickly check your work using wolfram alpha... and according to it, (0,0) is one but your other answers are wrong.
 

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