Thread: critical points of a multivariable function

For the life of me I just cant solve these two problems. I spent the last 2 hours trying to do it and I keep hitting a dead end, would someone be so kind and show me how.

What are the critical points of these functions, if any?
f(x,y)=-x^2-8xy-y^2
g(x,y)=x^2y-x^2-2y^2

Find the partial derivatives of f(x,y) and set them to zero. Same with g(x,y).