Help!!! find range, domain, max point on surface!!

Hello, I was wondering if you guys can help me understanding this problem.

f(x,y)=(11-x^2-y^2+4*x+2*y)^(1/2)

Find: Identify the surface, domain, range, plot the surface,and find the maximum point on the surface!

I know how to find the max point, if it's in 2D , just take the derivative and set it equal to zero. But how can I do it in 3D?

Thanks for your time,

[ for plotting, I am not sure, If I plot it in x, y I get the upper half of an ellipse, that mean in 3D it will be quadrant of an ellipse shape! ]