Find the critical point(s) of f(x,y) = x + y^2 - e^x. Decide which are extreme points and which are saddle points.

I got to here:

Px = 1 -e^x

Py = 2y

But now I'm stuck.

I know I'm supposed to use this rule:

d=fxxfyy-(fxy)^2

If d>0:

fxx(a,b)>0, then f(a, b) is a rel min

fxx(a,b)<0, then f(a,b) is a rel. max

If d<0, it's a saddle point.

Please help! Thank you