f(x, y) = 2x^3 + xy^2 + 5x^2 + y^2 + 8

Find the local max, min and saddle points of the function.

So far, I have:

-partial derivative of x= 6x^2 + y^2 + 10x

-partial derivative of y= 2xy+2y

But I'm really confused what to do next. My book says to set both of the partial derivative equations to 0 and then solve for one of the variables, but I get some weird answer that doesn't work in both equations.

Thanks so much for your help!