Determine the maximum and minimum of the function

in the square having corners at points and .

my progress:

derivate on x i get $\displaystyle 12x^2-6y$

derivate on y i get $\displaystyle 12y-6x$

idk if this is right thinking but i wanna solve x and i get

$\displaystyle y=6x/12$

so i got $\displaystyle 12x^2-6x/12=0$ and we get that x_1=0 and x_2=1/24 i am right or wrong and what shall i do next?