Given that, f(x,y)=2(x−y)2−x4−y4, we get On differentiating partially w.r.t. x, fx=4(x−y)−4x3 Again differentiating partially, we get fxx=4−12x2 ⇒(fxx)(0,0)=4−0=4 &=4−12y2 Similarly fyy=4−4 ⇒(fyy)(0,0)=4−0=4 and fxy=−4+0 ⇒(fxy)(0,0)=−4 ∴(fxxfyy−fxy2)(0,0)=4(4)−(−4)2=0
