What are the critical points? I've found the critical points:
$$f(x,y)={ x }^{ 3 }-3x-{ y }^{ 3 }+12y+2\\$$ $$\\ { f }_{ x }=0\\ { x }^{ 2 }-1=0\\ x=\pm 1\\ $$ $$\\ { f }_{ y }=0\\ { y }^{ 2 }-4=0\\ y=\pm 2$$
But I don't know what the y values are for x=±1 and what the x values are for y=±2. Any help? I've tried subbing in x=±1 in the original f(x,y) but I don't know what the y values are to sub in.
I keep getting: This post does not meet our quality standards. What am I supposed to fix? The character count?

You found that $x$ is $-1$ or $1$ and $y$ is $2$ or $-2$.  Therefore there are four critical points: $(-1,2), (-1,-2), (1, 2), (1, -2)$.  That's it.  When you set $f_x = 0$ and $f_y = 0$ you got equations with only $x$ or only $y$.
I don't see anything wrong with your question.  People post much worse questions here all the time.
