Identify and determine the nature of the critical points of

Identify and determine the nature of the critical points of the given function.
f(x,y) = x^2 +y^3 -6xy + 3x +6y

f/x = 2x - 6y + 3 = 0

f/y = 3y^2 - 6x + 6 = 0

y^2 - 2x + 2 = 0

y^2 - 6y + 5 = 0

y = 5 or 1

x = 13.5 or 1.5

(13.5,5) -> maxima

(1.5,1) -> minima