Seeds Of Chaos Console Commands

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Seeds Of Chaos Console Commands



 
 
 
 
 
 
 

Seeds Of Chaos Console Commands

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A comment on the website: I got through the staff page. ‘chaospower’ in the console, and was told that this command can be used to limit the Chaos damage your troops inflict. ‘chaospowerlevel’ in the console, and was told that this command can be used to limit the Chaos damage your troops inflict.

A comment on the website: I got through the staff page. ‘chaospower’ in the console, and was told that this command can be used to limit the Chaos damage your troops inflict. ‘chaospowerlevel’ in the console, and was told that this command can be used to limit the Chaos damage your troops inflict.Q:

Finding a saddle-point

I’ve been trying to do this problem for some time now and I can’t seem to figure out how to do it. I would have put it up as a new question but I don’t want to mess up anything.
Find a saddle point of $f: xy^2 + y^3 + 3x^2y + 4x^3$ on the curve $x^4 + y^4 + 12x^2y^2 = 1$ in the first quadrant.

A:

Let
$$f(x,y)=x(y^2+3x^2)+4(x^3+y)$$
So $x^4+y^4=1$ is the level curve.
Taking derivative of $f$ with respect to $x$ we get
$$2y^3+3x^2y-4=0$$
Taking derivative of $f$ with respect to $y$ we get
$$2y^2+3y-4x^2=0$$
Combining both conditions we get
$$2(y^3+y^2+3y+4x^2)=0$$
So for $z=x^2+y^2$, we get
$$2z(1+z-12z^2)=0$$
Taking $z=-1/2$, we get $x=-y=\pm\sqrt{1/8}$, that is $(0,0)$, $(1/8,1/8)$ and $(1/8,7/8)$
The second derivative

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