Finding Critical Points?

Question

I have to find the critical points and local extrema of the equation:

f(x,y)=y^3-3yx^2-3y^2-3x^2

When I it, I got (0,2) and (0,0) as critical points, but when looking at the solution my professor has posted, she also got (+-sqrt(3,-1) and I don't know how.

ted s · Answer

your δf / δx = - 6 x ( y + 1) = 0 ===> x = 0 OR y = - 1.......
δf /δy = 3 ( y² - 2 y - x²) = 0 ...if x = 0 then y = 0 or 2....if y = -1 then x² = 3...you finish

Finding Critical Points?

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