Answer: A
r = $\frac{\partial^2 f}{\partial x^2}$ = 2y
s = $\frac{\partial^2 f}{\partial x \partial y}$ = 2x - 3
t = $\frac{\partial^2 f}{\partial y^2}$ = 0
Since, rt - s^{2} <= 0, (if < 0 then we have no maxima or minima, if = 0 then we can't say anything).
Maxima will exist when rt - s^{2} > 0 and r < 0.
Minima will exist when rt - s^{2 }> 0 and r > 0.
Since, rt - s^{2} is never > 0 so we have no local extremum.