So I have $\displaystyle f(x,y)=x^3y+12x^2-8y$ and I need to find the maxima and minima. I calculated that $\displaystyle \bigtriangledown f = <3yx^2+24x,x^3-8>$, and by setting both to zero I figured out that there are critical points where $\displaystyle x = 0, x = -8/y, x=+-2$. Here's where I'm running into problems. I know how to find the x values, but I'm confused about how to find the corresponding y values for these critical points. For the first one, clearly y=0 when x = 0, but I'm not sure of the others because plugging them in to the 2 equations doesn't give me anything definite. In cases like this, what is the best way to find the corresponding y values of the critical points?