Consider a function f(x, y) : R2 -> R. The second-order Taylor series expansion f(x+Ax, y+ Ay) = f(x, y)+Axfx(x, y)+Ayfz(x, y)+ 7(x) fra(x, y) + , AxAyfou(x, y) +, Aryfur(x, y) +7 ( Ay) fuu(x, y) +. . . can be written as f(x + Ax, y + Ay) = f(x, y) + d (Ax, Ay) + (Ax, Ay) H(x, y) ( Ax, Ay) + ... where d E R2 is a column vector and H is a 2 by 2 matrix. Which one of the following statements is correct? [5 marks] as f( x, y ) a2 f (x, y ) axdy A d = (fx(x, y), fy(x, y) ) and H = as f (x,y) a2 f (x, y ) dyox ay2 a2 f (x, y) a2 f ( x, y) axdy B d = (fx(x, y), fy(x, y)) and H = a' f ( x,y) a f ( x, y ) dyor ay2 a2 f ( x, y ) a' f ( x, y ) axdy C d = (fx(x, y), fy(x, y)) and H = as f ( x, y ) a f (x, y ) dyor as f ( I, y) a2 f ( I, y ) axdy D d= (fx(x, y), - fy(x, y)) and H = a2 f ( x, y ) as f ( x, y ) a2 f ( x, y ) a2 f ( x, y) axdy Ed = (fx(x, y), fu(x, y)) and H = a2 f (x, y) a2 f ( x, y) ayor