Consider the function ( f(x, y) = x² y² + xy + x + 2y ). Find ( (x, y) ) for which ( ∇ f = 0 ). Express your answer as a function of ( x ). For which values of ( x ) is ( (x, y) ) a global minimum of ( f(x, y) )?
a) ( (x, yc) = (0, 0) ); ( x= 0 ); ( x ≤ 0 )
b) ( (x, y) = (1, -1) ); ( x= 1 ); ( x ≥ 1 )
c) ( (x, y) = (-1, 1) ); ( x= -1 ); ( x ≤ -1 )
d) ( (x, y) = (0, 0) ); ( x= 0 ); ( x ≥ 0 )