Find the critical point of $$ f(x,y) = 3x^3 + 3y^3 + x^3y^3 $$
To do this, I know that I need to set $$f_y = 0, f_x = 0 $$
So $$f_x= 9x^2 + 3x^2y^3$$ $$f_y = 9y^2 + 3y^2x^3$$
Then you solve for x, but substituting these two equations into each other.
But somehow I ended up with $$x = y$$ and thats not very helpful.
Is there something I did wrong or misunderstood?