Determine the maximum and minimum of the function

https://webwork.math.su.se/webwork2_...9ef36cb0b1.png

in the square having corners at points https://webwork.math.su.se/webwork2_...3eb6251e51.png and https://webwork.math.su.se/webwork2_...9aaad4a871.png.

my progress:

derivate on x i get

derivate on y i get

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

so i got and we get that x_1=0 and x_2=1/24 i am right or wrong and what shall i do next?